Also read this additional Example 4.

Also read this Maple Example that shows how to use Maple to step through Example 4.
Then use Maple as in this example to check your steps in the following problems.

Page 953, problems:

• 1, 3,

• 7 – 15 odd,

• 19    Hint:   x² – 4xy + 4y² + 2   =   (x – 2y)² + 2   ≥   2 , which shows that the absolute minimum of f is 2.

• 25, 37,      (use Maple as your graphing device),

• 41 – 45 odd,

• Also analyze all critical points of the function        f (x,y) = 3xy – x²y – xy².
  Answers:
  
  • (0,0) saddle point
  • (3,0) saddle point
  • (0,3) saddle point
  • (1,1) local maximum: f (1,1) = 1

• Also plot all the functions above using:
  • Maple examples of contour plots or
  • Maple examples of gradient field plots

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