Concept explainers
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 fx(2, 2) = fy(2, 2) = 0 implies that f has a
b. The function f could have a local maximum at (a, b) where
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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