Second Derivatives

Practice Questions

AP Calculus BC › Second Derivatives

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1

Determine the intervals on which the function is concave up:

$f=4\sin(\frac{x}{2})$

on the interval $0\leq x\leq 4\pi$

2

Determine the intervals on which the function is concave up:

$f=4\sin(\frac{x}{2})$

on the interval $0\leq x\leq 4\pi$

3

$\begin{align*}&\text{Calculate any and all points of inflection for: }\&f(x)=x^{2} - 6x + 2x^{3} - 2x^{4} + 6\end{align*}$

4

$\begin{align*}&\text{Calculate any and all points of inflection for: }\&f(x)=x^{2} - 6x + 2x^{3} - 2x^{4} + 6\end{align*}$

5

$\begin{align*}&\text{Calculate any and all points of inflection for: }\&f(x)=10x + 2^{(6x)} + 2x^{2} - 2x^{3}\end{align*}$

6

$\begin{align*}&\text{Calculate any and all points of inflection for: }\&f(x)=10x + 2^{(6x)} + 2x^{2} - 2x^{3}\end{align*}$

7

$\begin{align*}&\text{Find any points of inflection for the function:}\&3^{(3x)} - 4x + 10x^{3} + 10x^{4} + 2x^{5}\end{align*}$

8

$\begin{align*}&\text{Find any points of inflection for the function:}\&3^{(3x)} - 4x + 10x^{3} + 10x^{4} + 2x^{5}\end{align*}$

9

$\begin{align*}&\text{Find any points of inflection for the function:}\&2^{(3x)} - 6x + 2x^{2} - 7x^{3} - 9x^{5} + 1\end{align*}$

10

$\begin{align*}&\text{Find any points of inflection for the function:}\&2^{(3x)} - 6x + 2x^{2} - 7x^{3} - 9x^{5} + 1\end{align*}$

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