Explain why or why not Determine whether the
Chapter 12, Problem 61(choose chapter or problem)
Explain why or why not Determine whether the following statements are true and give an explanation or counterexample. Assume that f is differentiable at the points in question. a. The fact that fx12, 22 = fy12, 22 = 0 implies that f has a local maximum, local minimum, or saddle point at 12, 22. b. The function f could have a local maximum at 1a, b2 where fy1a, b2 _ 0. c. The function f could have both an absolute maximum and an absolute minimum at two different points that are not critical points. d. The tangent plane is horizontal at a point on a smooth surface corresponding to a critical point.
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