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