Determine whether the following statements are true or false: a)If f\'(x) = 0 at

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Determine whether the following statements are true or false: a)If f'(x) = 0 at each x of an open interval (a,b), then f(x) = C is a constant for all x in (a,b). b) Suppose that f is twice differentiable on an open interval I. If f' increases on I, then the graph of f is concave up. c)Suppose that f is twice differentiable on an open interval I. If f' decreasing on I, then the graph of f is concave down. d) For c in I, if f'(c) = 0 and f''(c) < 0 then f has a local min at x = c e) If the point (c,f(c)) is a point of inflection, then f''(c) = 0.

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