Suppose that f is twice differentiable satisfying (i) f (0) = 1, (ii) f (x) > 0 for all
Chapter 4, Problem 50(choose chapter or problem)
Suppose that f is twice differentiable satisfying (i) f (0) = 1, (ii) f (x) > 0 for all x = 0, and (iii) f (x) < 0 for x < 0 and f (x) > 0 for x > 0. Let g(x) = f (x2). (a) Sketch a possible graph of f . (b) Prove that g has no points of inflection and a unique local extreme value at x = 0. Sketch a possible graph of g. 51.
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