Let f(x) be continuous on [a,b]. Show that there exists a c in [a,b] such that f(c)=1/(b-a) times INTEGRAL(f(x)dx) (integral taken from a to b)

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Proof:

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My first thought is to use the Mean Value Theorem. BUT, the Mean Value Theorem requires that f be continuous AND differentiable. We are given continuity but not differentiability.

Any IDEAS?