Points of inflection

Practice Questions

AP Calculus AB › Points of inflection

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1

Determine the points of inflection of the following function:

$f(x)=\sin(x), 0 \leq x \leq 3\pi$

2

A computer code is written to detect points of inflection. The computer reports the following depending on what it finds:

$\alpha$ , if one point of inflection occurs at a positive x value;

$\beta$ , if one point of inflection occurs at a negative x value;

$\gamma$ , if more than one point of inflection occurs, regardless of the sign of x

What does the computer report for the following function:

$f=\frac{x^3}{6}+x^2$

3

Find the points of inflection of $f(x)=\frac{1}{12}x^4+\frac{1}{2}x^3-2x^2+6x-2$

4

Determine the points of inflection of the following function:

$g(x)=\frac{x^4}{12}+x^2$

5

Find all points of inflection for the equation .

6

For the function y, at which point(s) does the rate of _change_in the slope shift from decreasing to increasing.

7

Determine the points of inflection of the function:

$f=\frac{x^3}{3}-2x^2-6x$

8

At what value(s) does the following function have an inflection point?

9

Determine the points of inflection of the following function:

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

10

Determine the points of inflection for the following function:

$f=3\cos(2x), 0 \leq x \leq \pi$

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