# Lesson Worksheet: Convexity and Points of Inflection Mathematics • Higher Education

In this worksheet, we will practice determining the convexity of a function as well as its inflection points using its second derivative.

Q1:

Determine the intervals on which the function is concave up and down.

• AThe function is concave up on and and concave down on and .
• BThe function is concave up on and and concave down on and .
• CThe function is concave up on and and concave down on and .
• DThe function is concave up on and and concave down on and .
• EThe function is concave up on and and concave down on and .

Q2:

Use the given graph of to find the coordinates of the points of inflection. • A
• B,
• C
• D, ,
• E, ,

Q3:

Determine the inflection points of the curve .

• A
• B
• Chas no inflection points
• D

Q4:

Find the inflection point on the graph of .

• A
• B
• C
• Dno inflection point

Q5:

The figure shows the graph of for positive constants . Find the exact values of the constants if the local minimum value shown is and the inflection point occurs when .

• A,
• B,
• C,
• D,
• E,

Q6:

Determine the intervals on which is concave up and down.

• AThe function is concave down on the interval and up on the interval .
• BThe function is concave down on the interval and up on the interval .
• CThe function is concave down on the interval and up on the interval .
• DThe function is concave down on the interval and up on the interval .
• EThe function is concave down on the interval and up on the interval .

Q7:

Using the given graph of the function , at what values of does have inflection points? • A has inflection points when and .
• B has inflection points when , , and .
• C has inflection points when and .
• D has inflection points when and .
• E has inflection points when and .

Q8:

Given that , where , determine the inflection points of .

• A has inflection points at and .
• B has inflection points at and .
• C has inflection points at and .
• D has inflection points at and .
• E has inflection points at and .

Q9:

Find (if any) the inflection points of .

• A has an inflection point at .
• B has no inflection points.
• C has an inflection point at .
• D has an inflection point at .
• E has an inflection point at .

Q10:

Consider the parameric curve and . Determine whether this curve is concave up, down, or neither at .

• Aupward
• Bdownward
• Cneither

This lesson includes 90 additional questions and 543 additional question variations for subscribers.