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mean value theorem

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If f: [0, 1] -> R is differentiable on R and f' is continuous on [0, 1] with f(0)=0 and f'(x) > 0 for all x in [0, 1], prove that there exists c > 0 so that f(x) > cx for all x in (0, 1]

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Solution Summary

The mean value theorem is expressed.

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If f: [0, 1] -> R is differentiable on R and f' is continuous on [0, 1] with f(0)=0 and f'(x) > 0 for all x in [0, 1], prove that there exists c > 0 so that f(x) > cx for all x in (0, 1]

Proof:
The mean value theorem is as follows:
Let f : [a, b] → R be a continuous function on the ...

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