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Find $\displaystyle\lim_{x \to 0} \dfrac{e^{ 5x} - 1}{x}$ .
Find $\displaystyle\lim_{x \to 0} \dfrac{1 - \cos(6x)}{x^2}$ .
Find $\displaystyle\lim_{x \to 1} \dfrac{x^{ 7 } - 1}{\ln x}$ .
$f(x) = x^3 - 12x$ . At which $x$ does $f$ have a local maximum?
Here is the graph of the derivative $y = f'(x)$ . Tap the point of this graph at the $x$ -value where $f$ has a local maximum.
$f(x) = x^3 - 3x^2$ . At which $x$ does $f$ have an inflection point?
$f'(8) = 0$ and $f''(8) = 3$ . What happens at $x = 8$ ?
1. A local minimum
2. A local maximum
3. An inflection point
$f'(6) = 0$ and $f''(6) = 7$ . What happens at $x = 6$ ?
1. A local minimum
2. A local maximum
3. An inflection point
$f'(3) = 0$ and $f''(3) = 3$ . What happens at $x = 3$ ?
1. A local minimum
2. A local maximum
3. An inflection point
$f'(5) = 0$ and $f''(5) = 4$ . What happens at $x = 5$ ?
1. A local minimum
2. A local maximum
3. An inflection point
$f'(3) = 0$ and $f''(3) = 8$ . What happens at $x = 3$ ?
1. A local minimum
2. A local maximum
3. An inflection point
$f'(8) = 0$ and $f''(8) = 5$ . What happens at $x = 8$ ?
1. A local minimum
2. A local maximum
3. An inflection point
$f'(2) = 0$ and $f''(2) = 5$ . What happens at $x = 2$ ?
1. A local minimum
2. A local maximum
3. An inflection point
$f'(4) = 0$ and $f''(4) = 7$ . What happens at $x = 4$ ?
1. A local minimum
2. A local maximum
3. An inflection point
$f'(8) = 0$ and $f''(8) = 9$ . What happens at $x = 8$ ?
1. A local minimum
2. A local maximum
3. An inflection point
$f'(2) = 0$ and $f''(2) = 7$ . What happens at $x = 2$ ?
1. A local minimum
2. A local maximum
3. An inflection point
$f'(5) = 0$ and $f''(5) = 6$ . What happens at $x = 5$ ?
1. A local minimum
2. A local maximum
3. An inflection point
$f'(7) = 0$ and $f''(7) = 2$ . What happens at $x = 7$ ?
1. A local minimum
2. A local maximum
3. An inflection point
$f'(5) = 0$ and $f''(5) = 8$ . What happens at $x = 5$ ?
1. A local minimum
2. A local maximum
3. An inflection point
$f'(5) = 0$ and $f''(5) = 2$ . What happens at $x = 5$ ?
1. A local minimum
2. A local maximum
3. An inflection point
$f'(1) = 0$ and $f''(1) = 3$ . What happens at $x = 1$ ?
1. A local minimum
2. A local maximum
3. An inflection point
$f'(5) = 0$ and $f''(5) = 9$ . What happens at $x = 5$ ?
1. A local minimum
2. A local maximum
3. An inflection point
$f'(1) = 0$ and $f''(1) = 8$ . What happens at $x = 1$ ?
1. A local minimum
2. A local maximum
3. An inflection point
$f'(3) = 0$ and $f''(3) = 1$ . What happens at $x = 3$ ?
1. A local minimum
2. A local maximum
3. An inflection point
$f'(3) = 0$ and $f''(3) = 5$ . What happens at $x = 3$ ?
1. A local minimum
2. A local maximum
3. An inflection point
$f'(9) = 0$ and $f''(9) = 3$ . What happens at $x = 9$ ?
1. A local minimum
2. A local maximum
3. An inflection point
$f'(4) = 0$ and $f''(4) = 6$ . What happens at $x = 4$ ?
1. A local minimum
2. A local maximum
3. An inflection point
$f'(1) = 0$ and $f''(1) = 1$ . What happens at $x = 1$ ?
1. A local minimum
2. A local maximum
3. An inflection point
$f'(6) = 0$ and $f''(6) = 9$ . What happens at $x = 6$ ?
1. A local minimum
2. A local maximum
3. An inflection point
$f'(8) = 0$ and $f''(8) = 8$ . What happens at $x = 8$ ?
1. A local minimum
2. A local maximum
3. An inflection point
$f'(8) = 0$ and $f''(8) = 2$ . What happens at $x = 8$ ?
1. A local minimum
2. A local maximum
3. An inflection point
$f'(5) = 0$ and $f''(5) = 1$ . What happens at $x = 5$ ?
1. A local minimum
2. A local maximum
3. An inflection point
$f'(3) = 0$ and $f''(3) = 7$ . What happens at $x = 3$ ?
1. A local minimum
2. A local maximum
3. An inflection point
$f'(7) = 0$ and $f''(7) = 8$ . What happens at $x = 7$ ?
1. A local minimum
2. A local maximum
3. An inflection point
$f'(7) = 0$ and $f''(7) = 5$ . What happens at $x = 7$ ?
1. A local minimum
2. A local maximum
3. An inflection point
$f'(5) = 0$ and $f''(5) = 7$ . What happens at $x = 5$ ?
1. A local minimum
2. A local maximum
3. An inflection point
$f'(2) = 0$ and $f''(2) = 9$ . What happens at $x = 2$ ?
1. A local minimum
2. A local maximum
3. An inflection point
$f'(4) = 0$ and $f''(4) = 2$ . What happens at $x = 4$ ?
1. A local minimum
2. A local maximum
3. An inflection point
$f'(9) = 0$ and $f''(9) = 4$ . What happens at $x = 9$ ?
1. A local minimum
2. A local maximum
3. An inflection point
$f'(9) = 0$ and $f''(9) = 2$ . What happens at $x = 9$ ?
1. A local minimum
2. A local maximum
3. An inflection point
$f'(1) = 0$ and $f''(1) = 2$ . What happens at $x = 1$ ?
1. A local minimum
2. A local maximum
3. An inflection point
$f'(2) = 0$ and $f''(2) = 1$ . What happens at $x = 2$ ?
1. A local minimum
2. A local maximum
3. An inflection point
$f'(6) = 0$ and $f''(6) = 6$ . What happens at $x = 6$ ?
1. A local minimum
2. A local maximum
3. An inflection point
$f'(1) = 0$ and $f''(1) = 7$ . What happens at $x = 1$ ?
1. A local minimum
2. A local maximum
3. An inflection point
$f'(4) = 0$ and $f''(4) = 1$ . What happens at $x = 4$ ?
1. A local minimum
2. A local maximum
3. An inflection point
$f'(8) = 0$ and $f''(8) = 4$ . What happens at $x = 8$ ?
1. A local minimum
2. A local maximum
3. An inflection point
$f'(4) = 0$ and $f''(4) = 8$ . What happens at $x = 4$ ?
1. A local minimum
2. A local maximum
3. An inflection point
$f'(1) = 0$ and $f''(1) = 5$ . What happens at $x = 1$ ?
1. A local minimum
2. A local maximum
3. An inflection point
$f'(3) = 0$ and $f''(3) = 9$ . What happens at $x = 3$ ?
1. A local minimum
2. A local maximum
3. An inflection point
$f'(9) = 0$ and $f''(9) = 5$ . What happens at $x = 9$ ?
1. A local minimum
2. A local maximum
3. An inflection point
$f'(9) = 0$ and $f''(9) = 7$ . What happens at $x = 9$ ?
1. A local minimum
2. A local maximum
3. An inflection point
$f'(8) = 0$ and $f''(8) = 7$ . What happens at $x = 8$ ?
1. A local minimum
2. A local maximum
3. An inflection point
$f'(6) = 0$ and $f''(6) = 2$ . What happens at $x = 6$ ?
1. A local minimum
2. A local maximum
3. An inflection point
$f'(7) = 0$ and $f''(7) = 1$ . What happens at $x = 7$ ?
1. A local minimum
2. A local maximum
3. An inflection point
$f'(3) = 0$ and $f''(3) = 6$ . What happens at $x = 3$ ?
1. A local minimum
2. A local maximum
3. An inflection point
$f'(8) = 0$ and $f''(8) = 1$ . What happens at $x = 8$ ?
1. A local minimum
2. A local maximum
3. An inflection point
$f'(1) = 0$ and $f''(1) = 0$ . What can you conclude about $x = 1$ ?
1. Nothing yet: it could be a maximum, a minimum or neither
2. It is an inflection point
3. It is a local maximum
$f'(6) = 0$ and $f''(6) = 0$ . What can you conclude about $x = 6$ ?
1. Nothing yet: it could be a maximum, a minimum or neither
2. It is an inflection point
3. It is a local maximum
$f'(9) = 0$ and $f''(9) = 0$ . What can you conclude about $x = 9$ ?
1. Nothing yet: it could be a maximum, a minimum or neither
2. It is an inflection point
3. It is a local maximum
$f'(2) = 0$ and $f''(2) = 0$ . What can you conclude about $x = 2$ ?
1. Nothing yet: it could be a maximum, a minimum or neither
2. It is an inflection point
3. It is a local maximum
$f'(3) = 0$ and $f''(3) = 0$ . What can you conclude about $x = 3$ ?
1. Nothing yet: it could be a maximum, a minimum or neither
2. It is an inflection point
3. It is a local maximum
$f'(5) = 0$ and $f''(5) = 0$ . What can you conclude about $x = 5$ ?
1. Nothing yet: it could be a maximum, a minimum or neither
2. It is an inflection point
3. It is a local maximum
$f'(7) = 0$ and $f''(7) = 0$ . What can you conclude about $x = 7$ ?
1. Nothing yet: it could be a maximum, a minimum or neither
2. It is an inflection point
3. It is a local maximum
$f'(8) = 0$ and $f''(8) = 0$ . What can you conclude about $x = 8$ ?
1. Nothing yet: it could be a maximum, a minimum or neither
2. It is an inflection point
3. It is a local maximum
$f'(4) = 0$ and $f''(4) = 0$ . What can you conclude about $x = 4$ ?
1. Nothing yet: it could be a maximum, a minimum or neither
2. It is an inflection point
3. It is a local maximum
Find the maximum value of $f(x) = x^2 - 6x$ on $[0, 8]$ .
Find the minimum value of $f(x) = x^3 - 3x$ on $[0, 2]$ .
$f(x) = x^2$ on $[2, 5]$ . Find the $c$ given by the Mean Value Theorem.
$f(x) = x^3$ on $[0, 4]$ . Find the $c$ in $(0, 4)$ given by the Mean Value Theorem.
A car drove 276 miles in 4 hours. Must its speedometer have read exactly 69 mph at some moment?
1. Yes, by the Mean Value Theorem
2. Only if it drove at a constant speed
3. No: it may have gone faster and slower without hitting 69 exactly
A car drove 244 miles in 4 hours. Must its speedometer have read exactly 61 mph at some moment?
1. Yes, by the Mean Value Theorem
2. Only if it drove at a constant speed
3. No: it may have gone faster and slower without hitting 61 exactly
A car drove 268 miles in 4 hours. Must its speedometer have read exactly 67 mph at some moment?
1. Yes, by the Mean Value Theorem
2. Only if it drove at a constant speed
3. No: it may have gone faster and slower without hitting 67 exactly
A car drove 168 miles in 3 hours. Must its speedometer have read exactly 56 mph at some moment?
1. Yes, by the Mean Value Theorem
2. Only if it drove at a constant speed
3. No: it may have gone faster and slower without hitting 56 exactly
A car drove 220 miles in 4 hours. Must its speedometer have read exactly 55 mph at some moment?
1. Yes, by the Mean Value Theorem
2. Only if it drove at a constant speed
3. No: it may have gone faster and slower without hitting 55 exactly
A car drove 102 miles in 2 hours. Must its speedometer have read exactly 51 mph at some moment?
1. Yes, by the Mean Value Theorem
2. Only if it drove at a constant speed
3. No: it may have gone faster and slower without hitting 51 exactly
A car drove 153 miles in 3 hours. Must its speedometer have read exactly 51 mph at some moment?
1. Yes, by the Mean Value Theorem
2. Only if it drove at a constant speed
3. No: it may have gone faster and slower without hitting 51 exactly
A car drove 240 miles in 4 hours. Must its speedometer have read exactly 60 mph at some moment?
1. Yes, by the Mean Value Theorem
2. Only if it drove at a constant speed
3. No: it may have gone faster and slower without hitting 60 exactly
A car drove 216 miles in 4 hours. Must its speedometer have read exactly 54 mph at some moment?
1. Yes, by the Mean Value Theorem
2. Only if it drove at a constant speed
3. No: it may have gone faster and slower without hitting 54 exactly
A car drove 150 miles in 3 hours. Must its speedometer have read exactly 50 mph at some moment?
1. Yes, by the Mean Value Theorem
2. Only if it drove at a constant speed
3. No: it may have gone faster and slower without hitting 50 exactly
A car drove 177 miles in 3 hours. Must its speedometer have read exactly 59 mph at some moment?
1. Yes, by the Mean Value Theorem
2. Only if it drove at a constant speed
3. No: it may have gone faster and slower without hitting 59 exactly
A car drove 138 miles in 2 hours. Must its speedometer have read exactly 69 mph at some moment?
1. Yes, by the Mean Value Theorem
2. Only if it drove at a constant speed
3. No: it may have gone faster and slower without hitting 69 exactly
A car drove 120 miles in 2 hours. Must its speedometer have read exactly 60 mph at some moment?
1. Yes, by the Mean Value Theorem
2. Only if it drove at a constant speed
3. No: it may have gone faster and slower without hitting 60 exactly
A car drove 114 miles in 2 hours. Must its speedometer have read exactly 57 mph at some moment?
1. Yes, by the Mean Value Theorem
2. Only if it drove at a constant speed
3. No: it may have gone faster and slower without hitting 57 exactly
A car drove 232 miles in 4 hours. Must its speedometer have read exactly 58 mph at some moment?
1. Yes, by the Mean Value Theorem
2. Only if it drove at a constant speed
3. No: it may have gone faster and slower without hitting 58 exactly
A car drove 198 miles in 3 hours. Must its speedometer have read exactly 66 mph at some moment?
1. Yes, by the Mean Value Theorem
2. Only if it drove at a constant speed
3. No: it may have gone faster and slower without hitting 66 exactly
A car drove 165 miles in 3 hours. Must its speedometer have read exactly 55 mph at some moment?
1. Yes, by the Mean Value Theorem
2. Only if it drove at a constant speed
3. No: it may have gone faster and slower without hitting 55 exactly
A car drove 195 miles in 3 hours. Must its speedometer have read exactly 65 mph at some moment?
1. Yes, by the Mean Value Theorem
2. Only if it drove at a constant speed
3. No: it may have gone faster and slower without hitting 65 exactly
A car drove 204 miles in 3 hours. Must its speedometer have read exactly 68 mph at some moment?
1. Yes, by the Mean Value Theorem
2. Only if it drove at a constant speed
3. No: it may have gone faster and slower without hitting 68 exactly
A car drove 126 miles in 2 hours. Must its speedometer have read exactly 63 mph at some moment?
1. Yes, by the Mean Value Theorem
2. Only if it drove at a constant speed
3. No: it may have gone faster and slower without hitting 63 exactly
A car drove 212 miles in 4 hours. Must its speedometer have read exactly 53 mph at some moment?
1. Yes, by the Mean Value Theorem
2. Only if it drove at a constant speed
3. No: it may have gone faster and slower without hitting 53 exactly
A car drove 118 miles in 2 hours. Must its speedometer have read exactly 59 mph at some moment?
1. Yes, by the Mean Value Theorem
2. Only if it drove at a constant speed
3. No: it may have gone faster and slower without hitting 59 exactly
A car drove 183 miles in 3 hours. Must its speedometer have read exactly 61 mph at some moment?
1. Yes, by the Mean Value Theorem
2. Only if it drove at a constant speed
3. No: it may have gone faster and slower without hitting 61 exactly
A car drove 186 miles in 3 hours. Must its speedometer have read exactly 62 mph at some moment?
1. Yes, by the Mean Value Theorem
2. Only if it drove at a constant speed
3. No: it may have gone faster and slower without hitting 62 exactly
A car drove 124 miles in 2 hours. Must its speedometer have read exactly 62 mph at some moment?
1. Yes, by the Mean Value Theorem
2. Only if it drove at a constant speed
3. No: it may have gone faster and slower without hitting 62 exactly
A car drove 136 miles in 2 hours. Must its speedometer have read exactly 68 mph at some moment?
1. Yes, by the Mean Value Theorem
2. Only if it drove at a constant speed
3. No: it may have gone faster and slower without hitting 68 exactly
A car drove 171 miles in 3 hours. Must its speedometer have read exactly 57 mph at some moment?
1. Yes, by the Mean Value Theorem
2. Only if it drove at a constant speed
3. No: it may have gone faster and slower without hitting 57 exactly
A car drove 174 miles in 3 hours. Must its speedometer have read exactly 58 mph at some moment?
1. Yes, by the Mean Value Theorem
2. Only if it drove at a constant speed
3. No: it may have gone faster and slower without hitting 58 exactly
A car drove 122 miles in 2 hours. Must its speedometer have read exactly 61 mph at some moment?
1. Yes, by the Mean Value Theorem
2. Only if it drove at a constant speed
3. No: it may have gone faster and slower without hitting 61 exactly
A car drove 228 miles in 4 hours. Must its speedometer have read exactly 57 mph at some moment?
1. Yes, by the Mean Value Theorem
2. Only if it drove at a constant speed
3. No: it may have gone faster and slower without hitting 57 exactly
A car drove 112 miles in 2 hours. Must its speedometer have read exactly 56 mph at some moment?
1. Yes, by the Mean Value Theorem
2. Only if it drove at a constant speed
3. No: it may have gone faster and slower without hitting 56 exactly
A car drove 140 miles in 2 hours. Must its speedometer have read exactly 70 mph at some moment?
1. Yes, by the Mean Value Theorem
2. Only if it drove at a constant speed
3. No: it may have gone faster and slower without hitting 70 exactly
A car drove 134 miles in 2 hours. Must its speedometer have read exactly 67 mph at some moment?
1. Yes, by the Mean Value Theorem
2. Only if it drove at a constant speed
3. No: it may have gone faster and slower without hitting 67 exactly
A car drove 252 miles in 4 hours. Must its speedometer have read exactly 63 mph at some moment?
1. Yes, by the Mean Value Theorem
2. Only if it drove at a constant speed
3. No: it may have gone faster and slower without hitting 63 exactly
A car drove 100 miles in 2 hours. Must its speedometer have read exactly 50 mph at some moment?
1. Yes, by the Mean Value Theorem
2. Only if it drove at a constant speed
3. No: it may have gone faster and slower without hitting 50 exactly
A car drove 248 miles in 4 hours. Must its speedometer have read exactly 62 mph at some moment?
1. Yes, by the Mean Value Theorem
2. Only if it drove at a constant speed
3. No: it may have gone faster and slower without hitting 62 exactly
A car drove 180 miles in 3 hours. Must its speedometer have read exactly 60 mph at some moment?
1. Yes, by the Mean Value Theorem
2. Only if it drove at a constant speed
3. No: it may have gone faster and slower without hitting 60 exactly
A car drove 108 miles in 2 hours. Must its speedometer have read exactly 54 mph at some moment?
1. Yes, by the Mean Value Theorem
2. Only if it drove at a constant speed
3. No: it may have gone faster and slower without hitting 54 exactly
A car drove 264 miles in 4 hours. Must its speedometer have read exactly 66 mph at some moment?
1. Yes, by the Mean Value Theorem
2. Only if it drove at a constant speed
3. No: it may have gone faster and slower without hitting 66 exactly
A car drove 130 miles in 2 hours. Must its speedometer have read exactly 65 mph at some moment?
1. Yes, by the Mean Value Theorem
2. Only if it drove at a constant speed
3. No: it may have gone faster and slower without hitting 65 exactly
A car drove 162 miles in 3 hours. Must its speedometer have read exactly 54 mph at some moment?
1. Yes, by the Mean Value Theorem
2. Only if it drove at a constant speed
3. No: it may have gone faster and slower without hitting 54 exactly
A car drove 156 miles in 3 hours. Must its speedometer have read exactly 52 mph at some moment?
1. Yes, by the Mean Value Theorem
2. Only if it drove at a constant speed
3. No: it may have gone faster and slower without hitting 52 exactly
A car drove 106 miles in 2 hours. Must its speedometer have read exactly 53 mph at some moment?
1. Yes, by the Mean Value Theorem
2. Only if it drove at a constant speed
3. No: it may have gone faster and slower without hitting 53 exactly
A car drove 200 miles in 4 hours. Must its speedometer have read exactly 50 mph at some moment?
1. Yes, by the Mean Value Theorem
2. Only if it drove at a constant speed
3. No: it may have gone faster and slower without hitting 50 exactly
A car drove 192 miles in 3 hours. Must its speedometer have read exactly 64 mph at some moment?
1. Yes, by the Mean Value Theorem
2. Only if it drove at a constant speed
3. No: it may have gone faster and slower without hitting 64 exactly
A car drove 116 miles in 2 hours. Must its speedometer have read exactly 58 mph at some moment?
1. Yes, by the Mean Value Theorem
2. Only if it drove at a constant speed
3. No: it may have gone faster and slower without hitting 58 exactly
A car drove 132 miles in 2 hours. Must its speedometer have read exactly 66 mph at some moment?
1. Yes, by the Mean Value Theorem
2. Only if it drove at a constant speed
3. No: it may have gone faster and slower without hitting 66 exactly
A car drove 272 miles in 4 hours. Must its speedometer have read exactly 68 mph at some moment?
1. Yes, by the Mean Value Theorem
2. Only if it drove at a constant speed
3. No: it may have gone faster and slower without hitting 68 exactly
A car drove 280 miles in 4 hours. Must its speedometer have read exactly 70 mph at some moment?
1. Yes, by the Mean Value Theorem
2. Only if it drove at a constant speed
3. No: it may have gone faster and slower without hitting 70 exactly
A car drove 204 miles in 4 hours. Must its speedometer have read exactly 51 mph at some moment?
1. Yes, by the Mean Value Theorem
2. Only if it drove at a constant speed
3. No: it may have gone faster and slower without hitting 51 exactly
A particle's position is $s(t) = t^2 - 2t$ . At what time $t$ is it at rest?
At $t = 3$ , a particle has velocity $-8$ m/s and acceleration $-2$ m/s². Is it speeding up or slowing down?
1. Speeding up: velocity and acceleration have the same sign
2. Slowing down, because the acceleration is negative
3. Neither: its speed stays the same
At $t = 3$ , a particle has velocity $-7$ m/s and acceleration $-2$ m/s². Is it speeding up or slowing down?
1. Speeding up: velocity and acceleration have the same sign
2. Slowing down, because the acceleration is negative
3. Neither: its speed stays the same
At $t = 3$ , a particle has velocity $-3$ m/s and acceleration $-8$ m/s². Is it speeding up or slowing down?
1. Speeding up: velocity and acceleration have the same sign
2. Slowing down, because the acceleration is negative
3. Neither: its speed stays the same
At $t = 3$ , a particle has velocity $-3$ m/s and acceleration $-3$ m/s². Is it speeding up or slowing down?
1. Speeding up: velocity and acceleration have the same sign
2. Slowing down, because the acceleration is negative
3. Neither: its speed stays the same
At $t = 3$ , a particle has velocity $-3$ m/s and acceleration $-9$ m/s². Is it speeding up or slowing down?
1. Speeding up: velocity and acceleration have the same sign
2. Slowing down, because the acceleration is negative
3. Neither: its speed stays the same
At $t = 3$ , a particle has velocity $-7$ m/s and acceleration $-4$ m/s². Is it speeding up or slowing down?
1. Speeding up: velocity and acceleration have the same sign
2. Slowing down, because the acceleration is negative
3. Neither: its speed stays the same
At $t = 3$ , a particle has velocity $-8$ m/s and acceleration $-6$ m/s². Is it speeding up or slowing down?
1. Speeding up: velocity and acceleration have the same sign
2. Slowing down, because the acceleration is negative
3. Neither: its speed stays the same
At $t = 3$ , a particle has velocity $-5$ m/s and acceleration $-5$ m/s². Is it speeding up or slowing down?
1. Speeding up: velocity and acceleration have the same sign
2. Slowing down, because the acceleration is negative
3. Neither: its speed stays the same
At $t = 3$ , a particle has velocity $-1$ m/s and acceleration $-7$ m/s². Is it speeding up or slowing down?
1. Speeding up: velocity and acceleration have the same sign
2. Slowing down, because the acceleration is negative
3. Neither: its speed stays the same
At $t = 3$ , a particle has velocity $-9$ m/s and acceleration $-8$ m/s². Is it speeding up or slowing down?
1. Speeding up: velocity and acceleration have the same sign
2. Slowing down, because the acceleration is negative
3. Neither: its speed stays the same
At $t = 3$ , a particle has velocity $-6$ m/s and acceleration $-7$ m/s². Is it speeding up or slowing down?
1. Speeding up: velocity and acceleration have the same sign
2. Slowing down, because the acceleration is negative
3. Neither: its speed stays the same
At $t = 3$ , a particle has velocity $-2$ m/s and acceleration $-9$ m/s². Is it speeding up or slowing down?
1. Speeding up: velocity and acceleration have the same sign
2. Slowing down, because the acceleration is negative
3. Neither: its speed stays the same
At $t = 3$ , a particle has velocity $-1$ m/s and acceleration $-4$ m/s². Is it speeding up or slowing down?
1. Speeding up: velocity and acceleration have the same sign
2. Slowing down, because the acceleration is negative
3. Neither: its speed stays the same
At $t = 3$ , a particle has velocity $-1$ m/s and acceleration $-6$ m/s². Is it speeding up or slowing down?
1. Speeding up: velocity and acceleration have the same sign
2. Slowing down, because the acceleration is negative
3. Neither: its speed stays the same
At $t = 3$ , a particle has velocity $-4$ m/s and acceleration $-4$ m/s². Is it speeding up or slowing down?
1. Speeding up: velocity and acceleration have the same sign
2. Slowing down, because the acceleration is negative
3. Neither: its speed stays the same
At $t = 3$ , a particle has velocity $-6$ m/s and acceleration $-4$ m/s². Is it speeding up or slowing down?
1. Speeding up: velocity and acceleration have the same sign
2. Slowing down, because the acceleration is negative
3. Neither: its speed stays the same
At $t = 3$ , a particle has velocity $-4$ m/s and acceleration $-8$ m/s². Is it speeding up or slowing down?
1. Speeding up: velocity and acceleration have the same sign
2. Slowing down, because the acceleration is negative
3. Neither: its speed stays the same
At $t = 3$ , a particle has velocity $-3$ m/s and acceleration $-5$ m/s². Is it speeding up or slowing down?
1. Speeding up: velocity and acceleration have the same sign
2. Slowing down, because the acceleration is negative
3. Neither: its speed stays the same
At $t = 3$ , a particle has velocity $-4$ m/s and acceleration $-3$ m/s². Is it speeding up or slowing down?
1. Speeding up: velocity and acceleration have the same sign
2. Slowing down, because the acceleration is negative
3. Neither: its speed stays the same
At $t = 3$ , a particle has velocity $-6$ m/s and acceleration $-3$ m/s². Is it speeding up or slowing down?
1. Speeding up: velocity and acceleration have the same sign
2. Slowing down, because the acceleration is negative
3. Neither: its speed stays the same
At $t = 3$ , a particle has velocity $-3$ m/s and acceleration $-1$ m/s². Is it speeding up or slowing down?
1. Speeding up: velocity and acceleration have the same sign
2. Slowing down, because the acceleration is negative
3. Neither: its speed stays the same
At $t = 3$ , a particle has velocity $-2$ m/s and acceleration $-8$ m/s². Is it speeding up or slowing down?
1. Speeding up: velocity and acceleration have the same sign
2. Slowing down, because the acceleration is negative
3. Neither: its speed stays the same
At $t = 3$ , a particle has velocity $-7$ m/s and acceleration $-7$ m/s². Is it speeding up or slowing down?
1. Speeding up: velocity and acceleration have the same sign
2. Slowing down, because the acceleration is negative
3. Neither: its speed stays the same
At $t = 3$ , a particle has velocity $-2$ m/s and acceleration $-7$ m/s². Is it speeding up or slowing down?
1. Speeding up: velocity and acceleration have the same sign
2. Slowing down, because the acceleration is negative
3. Neither: its speed stays the same
At $t = 3$ , a particle has velocity $-1$ m/s and acceleration $-9$ m/s². Is it speeding up or slowing down?
1. Speeding up: velocity and acceleration have the same sign
2. Slowing down, because the acceleration is negative
3. Neither: its speed stays the same
At $t = 3$ , a particle has velocity $-8$ m/s and acceleration $-5$ m/s². Is it speeding up or slowing down?
1. Speeding up: velocity and acceleration have the same sign
2. Slowing down, because the acceleration is negative
3. Neither: its speed stays the same
At $t = 3$ , a particle has velocity $-9$ m/s and acceleration $-1$ m/s². Is it speeding up or slowing down?
1. Speeding up: velocity and acceleration have the same sign
2. Slowing down, because the acceleration is negative
3. Neither: its speed stays the same
At $t = 3$ , a particle has velocity $-4$ m/s and acceleration $-6$ m/s². Is it speeding up or slowing down?
1. Speeding up: velocity and acceleration have the same sign
2. Slowing down, because the acceleration is negative
3. Neither: its speed stays the same
At $t = 3$ , a particle has velocity $-5$ m/s and acceleration $-6$ m/s². Is it speeding up or slowing down?
1. Speeding up: velocity and acceleration have the same sign
2. Slowing down, because the acceleration is negative
3. Neither: its speed stays the same
At $t = 3$ , a particle has velocity $-8$ m/s and acceleration $-3$ m/s². Is it speeding up or slowing down?
1. Speeding up: velocity and acceleration have the same sign
2. Slowing down, because the acceleration is negative
3. Neither: its speed stays the same
At $t = 3$ , a particle has velocity $-9$ m/s and acceleration $-3$ m/s². Is it speeding up or slowing down?
1. Speeding up: velocity and acceleration have the same sign
2. Slowing down, because the acceleration is negative
3. Neither: its speed stays the same
At $t = 3$ , a particle has velocity $-2$ m/s and acceleration $-1$ m/s². Is it speeding up or slowing down?
1. Speeding up: velocity and acceleration have the same sign
2. Slowing down, because the acceleration is negative
3. Neither: its speed stays the same
At $t = 3$ , a particle has velocity $-8$ m/s and acceleration $-1$ m/s². Is it speeding up or slowing down?
1. Speeding up: velocity and acceleration have the same sign
2. Slowing down, because the acceleration is negative
3. Neither: its speed stays the same
At $t = 3$ , a particle has velocity $-5$ m/s and acceleration $-4$ m/s². Is it speeding up or slowing down?
1. Speeding up: velocity and acceleration have the same sign
2. Slowing down, because the acceleration is negative
3. Neither: its speed stays the same
At $t = 3$ , a particle has velocity $-5$ m/s and acceleration $-9$ m/s². Is it speeding up or slowing down?
1. Speeding up: velocity and acceleration have the same sign
2. Slowing down, because the acceleration is negative
3. Neither: its speed stays the same
At $t = 3$ , a particle has velocity $-3$ m/s and acceleration $-6$ m/s². Is it speeding up or slowing down?
1. Speeding up: velocity and acceleration have the same sign
2. Slowing down, because the acceleration is negative
3. Neither: its speed stays the same
At $t = 3$ , a particle has velocity $-5$ m/s and acceleration $-1$ m/s². Is it speeding up or slowing down?
1. Speeding up: velocity and acceleration have the same sign
2. Slowing down, because the acceleration is negative
3. Neither: its speed stays the same
At $t = 3$ , a particle has velocity $-8$ m/s and acceleration $-7$ m/s². Is it speeding up or slowing down?
1. Speeding up: velocity and acceleration have the same sign
2. Slowing down, because the acceleration is negative
3. Neither: its speed stays the same
At $t = 3$ , a particle has velocity $-5$ m/s and acceleration $-2$ m/s². Is it speeding up or slowing down?
1. Speeding up: velocity and acceleration have the same sign
2. Slowing down, because the acceleration is negative
3. Neither: its speed stays the same
At $t = 3$ , a particle has velocity $-1$ m/s and acceleration $-1$ m/s². Is it speeding up or slowing down?
1. Speeding up: velocity and acceleration have the same sign
2. Slowing down, because the acceleration is negative
3. Neither: its speed stays the same
At $t = 3$ , a particle has velocity $-6$ m/s and acceleration $-1$ m/s². Is it speeding up or slowing down?
1. Speeding up: velocity and acceleration have the same sign
2. Slowing down, because the acceleration is negative
3. Neither: its speed stays the same
At $t = 3$ , a particle has velocity $-9$ m/s and acceleration $-2$ m/s². Is it speeding up or slowing down?
1. Speeding up: velocity and acceleration have the same sign
2. Slowing down, because the acceleration is negative
3. Neither: its speed stays the same
At $t = 3$ , a particle has velocity $-2$ m/s and acceleration $-2$ m/s². Is it speeding up or slowing down?
1. Speeding up: velocity and acceleration have the same sign
2. Slowing down, because the acceleration is negative
3. Neither: its speed stays the same
At $t = 3$ , a particle has velocity $-9$ m/s and acceleration $-4$ m/s². Is it speeding up or slowing down?
1. Speeding up: velocity and acceleration have the same sign
2. Slowing down, because the acceleration is negative
3. Neither: its speed stays the same
At $t = 3$ , a particle has velocity $-1$ m/s and acceleration $-8$ m/s². Is it speeding up or slowing down?
1. Speeding up: velocity and acceleration have the same sign
2. Slowing down, because the acceleration is negative
3. Neither: its speed stays the same
At $t = 3$ , a particle has velocity $-6$ m/s and acceleration $-6$ m/s². Is it speeding up or slowing down?
1. Speeding up: velocity and acceleration have the same sign
2. Slowing down, because the acceleration is negative
3. Neither: its speed stays the same
At $t = 3$ , a particle has velocity $-9$ m/s and acceleration $-5$ m/s². Is it speeding up or slowing down?
1. Speeding up: velocity and acceleration have the same sign
2. Slowing down, because the acceleration is negative
3. Neither: its speed stays the same
At $t = 3$ , a particle has velocity $-8$ m/s and acceleration $-4$ m/s². Is it speeding up or slowing down?
1. Speeding up: velocity and acceleration have the same sign
2. Slowing down, because the acceleration is negative
3. Neither: its speed stays the same
At $t = 3$ , a particle has velocity $-3$ m/s and acceleration $-7$ m/s². Is it speeding up or slowing down?
1. Speeding up: velocity and acceleration have the same sign
2. Slowing down, because the acceleration is negative
3. Neither: its speed stays the same
At $t = 3$ , a particle has velocity $-2$ m/s and acceleration $-5$ m/s². Is it speeding up or slowing down?
1. Speeding up: velocity and acceleration have the same sign
2. Slowing down, because the acceleration is negative
3. Neither: its speed stays the same
A particle's position is $s(t) = t^2 - 4t$ meters. Find the total distance it travels from $t = 0$ to $t = 9$ .
A farmer has 104 m of fence for three sides of a rectangle; a long wall forms the fourth side. Find the largest possible area, in m².
Two positive numbers add up to 35. What is the largest possible value of their product?
Squares of side $x$ are cut from the corners of a 9-cm square sheet, and the sides are folded up into an open box. Which $x$ gives the largest volume?

Answers

$5$
$18$
$7$
$-2$
$(-3, 0)$
$1$
A local minimum
Nothing yet: it could be a maximum, a minimum or neither
$16$
$-2$
$\frac{7}{2}$
$\frac{4 \sqrt{3}}{3}$
Yes, by the Mean Value Theorem
$1$
Speeding up: velocity and acceleration have the same sign
$53$
$1352$
$\frac{1225}{4}$
$\frac{3}{2}$