Exercises

1. Describe the contours of a function near a critical point that is a local extremum. How do they differ from the contours near a critical point that is a saddle point?
2. Find and classify the critical points of the following functions.
   1. .
   2. .
   3. .
3. The function

   

   has three critical points. Locate and classify them.

4. The function

   

   has five critical points. Locate and classify them.