This lesson includes 54 additional questions and 406 additional question variations for subscribers.

# Lesson Worksheet: Critical Points and Local Extrema of a Function Mathematics • Higher Education

In this worksheet, we will practice finding critical points of a function and checking for local extrema using the first derivative test.

**Q4: **

Determine, if any, the local maximum and minimum values of , together with where they occur.

- AThe local maximum is at , and there is no local minimum.
- BThe local maximum is at , and the local minimum is at .
- CThe local minimum is at , and there is no local maximum.
- DThe local minimum is at , and the local maximum is at .

**Q7: **

The graph of the first derivative of a continuous function is shown. At what values of does have a local maximum and a local minimum?

- A has local maximum points at and and a local minimum point at .
- B has local maximum points at and and local minimum points at and .
- C has a local maximum point at and local minimum points at and .
- D has local maximum points at and and a local minimum point at .
- E has local maximum points at and and local minimum points at and .