Second Derivatives

Practice Questions

AP Calculus AB › Second Derivatives

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1

On a closed interval, the function is decreasing. What can we say about and on these intervals?

2

$\begin{align*}&\text{For the point }x=4\text{, find the concavity of the function}\&y=-20tan(3x)\end{align*}$

3

$f(x) = x^{3}+ 4x^{2}+ 8x- 17$

A relative minimum of the graph of can be located at (nearest hundredth):

4

$\begin{align*}&\text{For the point }x=4\text{, find the concavity of the function}\&y=-20tan(3x)\end{align*}$

5

$f(x) = x^{3}+ 4x^{2}+ 8x- 17$

A relative minimum of the graph of can be located at (nearest hundredth):

6

On a closed interval, the function is decreasing. What can we say about and on these intervals?

7

Determine the intervals on which the following function is concave up:

$f(x)= \frac{x^4}{12}+\frac{x^3}{2}-2x^2$

8

Determine the intervals on which the function is concave up:

$f=\frac{x^4}{6}-25x^2$

9

Find the second derivative.

10

Determine the intervals on which the function is concave up:

$f=\frac{x^4}{6}-25x^2$

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