Definition of Differentiation (College Board AP® Calculus AB)

Exam Questions

14 mins10 questions

2 marks

$t$ (hours)	0	3	7	10	12
$r^{'} (t)$ (centimeters per hour)	-3.2	-2.5	-2.1	-1.6	-1.4

$t$

(hours)

$r^{'} (t)$

(centimeters per hour)

-3.2

-2.5

-2.1

-1.6

-1.4

The radius of a puddle as it dries up is given by a twice-differentiable function $r$ , where $r (t)$ is measured in centimeters and $t$ is measured in hours. The table above gives selected values of $r^{'} (t)$ , the rate of change of the radius, over the time interval $0 \leq t \leq 12$ .

Approximate $r^{''} (5)$ using the average rate of change of $r'$ over the interval $3 \leq t \leq 7$ . Show the computations that lead to your answer, and indicate units of measure.

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1 mark

$t$ (minutes)	0	12	20	24	40
$v (t)$ (meters per minute)	0	240	280	250	180

$t$

(minutes)

$v (t)$

(meters per minute)

240

280

250

180

A dog runs along a straight path. For $0 \leq t \leq 40$ , the dog's velocity is given by a differentiable function $v$ .

Selected values of $v (t)$ , where $t$ is measured in minutes and $v (t)$ is measured in meters per minute, are given in the table above.

Use the data in the table to estimate the value of $v^{'} (22)$ .

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