AP Calculus Applications of Derivatives

Question 1

Let f\left(x\right)=x^3+5x for what x in \left[1,3\right] does instantaneous rate of change equal average rate of change

Accepted Answer

\sqrt{\frac{13}{3}}

Question 2

Paint spills in a circle with radius increasing at 2.5 in/min, how fast in area increasing when radius is 18 inches?

Accepted Answer

90\pi in^2/\min

Question 3

If f\left(5\right)=3 and f'\left(5\right)=4, estimate f\left(4.8\right) using local linear approximation for f at x=5

Accepted Answer

2.2

Question 4

P\left(t\right) is population size at time tWhich describes linear growth in population size?

Accepted Answer

\frac{dP}{dt}=200

Question 5

Which is true about y=\ln\left|x^2-1\right| on the interval \left(-1,1\right)

Accepted Answer

It is concave down

Question 6

The absolute maximum value of f\left(x\right)=x^3-3x^2+12 on \left[-2,4\right] occurs at x=

Accepted Answer

4

Question 7

Given f''\left(x\right) in the table below, which statement is true?

Accepted Answer

f\left(x\right) changes concavity in interval \left(0,2\right)

Question 8

A particle's velocity is given by \frac{dx}{dt}=-10t^4+9t^2+8tIts acceleration is zero when t=

Accepted Answer

0.831

Question 9

A rectangle has vertices on the graph y=\cos xwhat is the maximum shaded area?

Accepted Answer

0.878

Question 10

A particle moves so its position is x\left(t\right)=t^2-6t+5at what time is its velocity zero?

Accepted Answer

3

Question 11

Let f\left(x\right)=x^3-2x^2+5x-16 what x in \left[0,5\right] does instantaneous rate equal average rate

Accepted Answer

3

Questions 11