Relationship between the concavity of ƒ and the sign of ƒ''

Practice Questions

AP Calculus AB › Relationship between the concavity of ƒ and the sign of ƒ''

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1

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

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

2

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

3

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

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

4

Find the second derivative.

5

Determine the intervals on which the function is concave up:

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

6

Determine the intervals on which the function is concave up:

$f=\frac{x^5}{20}-4x^2$

7

Determine the intervals on which the function is concave up:

$f=\frac{x^7}{42}-\frac{x^5}{20}-\frac{x^3}{6}+\frac{x^2}{2}$

8

What is the concavity of at x=1?

9

Explain whether f(x) is concave up or concave down when , and choose the correct explanation for its behavior.

10

Determine the intervals on which the function is concave down:

$f=\frac{x^5}{20}+\frac{x^4}{12}+\frac{x^3}{6}+2x^2$

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