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Lesson: Concavity and Points of Inflection

In this lesson, we will learn how to determine the concavity of functions as well as their inflection points.

Worksheet • 25 Questions

Q1:

Find (if any) the inflection points of .

AThere are no inflection points.
BThe inflection point is .
CThe inflection point is .
DThe inflection point is .
EThe inflection point is .

Q2:

Determine where is concave up and where it is concave down.

A The function is concave up on the intervals and and down on the interval .
B The function is concave up on the intervals and and down on the interval .
C The function is concave up on the interval and down on the intervals and .
D The function is concave up on the intervals and and down on the interval .
E The function is concave up on the interval and down on the intervals and .

Q3:

For , determine the intervals on which is concave up and concave down.

A is concave up on the interval and concave down on the intervals and .
B is concave up on the interval and concave down on the interval .
C is concave up on the intervals and and concave down on the interval .
D is concave up on the intervals and and concave down on the interval .
E is concave up on the interval and concave down on the intervals and .

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