[This problem illustrates the fact that f _ (c) = 0 is not a sufficient condition for
Chapter 5, Problem 17(choose chapter or problem)
[This problem illustrates the fact that f _ (c) = 0 is not a sufficient condition for the existence of a local extremum of a differentiable function.] Show that the function f (x) = x3 has a horizontal tangent at x = 0; that is, show that f _ (0) = 0, but f _ (x) does not change sign at x = 0 and, hence, f (x) does not have a local extremum at x = 0.
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