# Worksheet: Second Derivative Test for Local Extrema

In this worksheet, we will practice classifying local extrema using the second derivative test.

**Q1: **

Find, if any, the points where has a local maximum or local minimum.

- Ais the local minimum point, and the function does not have a local maximum point.
- Bis the local maximum point, and is the local minimum point.
- Cis the local minimum point, and the function does not have a local maximum point.
- Dis the local maximum point, and the function does not have a local minimum point.
- Eis the local minimum point, and is the local maximum point.

**Q2: **

Find, if any, the point where has a local maximum or local minimum.

- Ais a local maximum point.
- Bis a local minimum point.
- Cis a local minimum point.
- DThe function does not have local maximum or minimum points.
- Eis a local maximum point.

**Q6: **

Determine the local maximum and local minimum values of .

- Alocal maximum value at , local minimum value at
- Blocal maximum value 8 at , local minimum value 8 at
- Clocal maximum value at , local minimum value 3 at
- Dlocal maximum value 8 at , local minimum value 8 at
- Elocal maximum value 3 at , local minimum value at

**Q10: **

Find, if any, the local maximum and local minimum values of .

- AThe function does not have local maximum or minimum points.
- BThe local maximum value is.
- CThe local maximum value is, and the local minimum value is.
- DThe local minimum value is, and the local maximum value is.
- EThe local minimum value is.

**Q11: **

Find the local maxima and local minima of , if any.

- Alocal minimum at , local maximum at
- Blocal minimum at , local maximum at
- Clocal minimum at , local maximum at
- Dlocal minimum at , local maximum at
- Elocal minimum at , local maximum at

**Q12: **

Find the local maximum and minimum values of .

- Alocal minimum 0 at
- Blocal maximum 0 at
- Clocal minimum at
- Dno local maximum and no local minimum values
- Elocal maximum at

**Q14: **

Find, if any, the local maximum and local minimum values of , together with their type.

- Aabsolute maximum is , absolute minimum is
- Babsolute maximum is , absolute minimum is
- Cabsolute maximum is , absolute minimum is
- Dabsolute maximum is , absolute minimum is

**Q15: **

Find the coordinates of all the local minima and maxima of the function .

- AThere are no local minima or maxima values.
- BLocal minima at and local maxima at
- CLocal minima at
- DLocal minima at
- ELocal minima at and local maxima at