Question: Let f : [a, b] R be continuous on the closed, bounded interval [a.b]. Also assume that f is differentiable on the open interval (a,

Let f : [a, b] R be continuous on the closed, bounded interval [a.b]. Also assume that f is differentiable on the open interval (a, b).

Assume that there exists a number c R so

f(x) c for x a+ .

Show that f is differentiable at the endpoint a with f (a) = c.

Use the mean value theorem.

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