Practices on Max/Min.

1. Find the relative extrema for the following functions:

1. [Ans: Set and no critical number]

2. [Ans: no crical number]

3. [Ans: Set yields, the crical number at Since and has a local minimum at

4. [Ans: has a local minimum at . ]

5. [Ans: has a local minimum at ]

6. [Ans: has a relative maximum at .]

7. [Ans: has a saddle point at and a relative minimum at ]

8. [Ans: has a saddle point at and a relative minimum at ]

9. [Ans: has a relative minimum at ]

10. [Ans: has saddle points at and ]

2. Use Maple to sketch the contour map (collections of the level curves for ) for problems (g) through (j) above.

3. Given the following surface determined by the function find if is a curve on the surface.

1. . (where and are constants). [Ans: ]

2. [Ans: ]

3. (where and are constants) [Ans:

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