# Worksheet: Extrema of a Multivariable Function

In this worksheet, we will practice finding critical points of a multivariable function and identifying the local maximum, local minimum, and saddle points of the function.

**Q5: **

Find all stationary points of the function .

- A is a local minimum point, and are local maximum points, and is a saddle point.
- B is a local minimum point, is a local maximum point, and and are saddle points.
- C is a local minimum point, is a local maximum point, and and are saddle points.
- D and are local mimimum points, is a local maximum point, and is a saddle point.
- E is a local minimum point, is a local maximum point, and and are saddle points.

**Q8: **

Find all stationary points of the function , stating whether they are minima, maxima, or saddle points.

- A is a local minimum point and is a saddle point.
- B is a local maximum point and is a saddle point.
- C is a local minimum point and is a saddle point.
- D is a local maximum point and is a saddle point.
- E is a local minimum point and is a saddle point.

**Q9: **

Find all stationary points of the function , stating whether they are minima, maxima, or saddle points.

- A is a local minimum point and is a saddle point.
- B is a local minimum point and is a saddle point.
- C is a local minimum point and is a saddle point.
- D is a local minimum point and is a saddle point.
- E is a local minimum point and is a saddle point.

**Q10: **

Find all stationary points of the function , stating whether they are minima, maxima, or saddle points.

- A and are local minimum points, is a local maximum point, and is a saddle point.
- B is a local minimum point, is a local maximum point, and and are saddle points.
- C is a local minimum point, and are local maximum points, and is a saddle point.
- D is a local minimum point, is a local maximum point, and and are saddle points.
- E is a local minimum point, is a local maximum point, and and are saddle points.