f:[a,b]->R is continuous on [a,b] and differentiable on (a,b). Show , then f'(a) exists and equals A.

The hint we got was to use the definition of f'(a) and the Mean Value theorem, but I"m still having no luck. Can someone please help?

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- Oct 30th 2008, 01:49 PMhockey777Differentiation (Real Analysis)
f:[a,b]->R is continuous on [a,b] and differentiable on (a,b). Show , then f'(a) exists and equals A.

The hint we got was to use the definition of f'(a) and the Mean Value theorem, but I"m still having no luck. Can someone please help? - Oct 30th 2008, 02:43 PMPlato
Suppose that because , we know that .

By the mean value theorem: .

Now look at this:

- Oct 30th 2008, 04:57 PMhockey777
NM, dumb post.

- Oct 30th 2008, 05:32 PMPlato