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I've received this task from my professor to solve for an assignment, but I do not know how to prove it.

Asume the functions f and g are so that f' and g' are continuous on the interval [a,b] and f'' and g'' exist on (a, b).

Asume further that f'(a) = g'(a) & f'(b) = g'(b).

Prove that there is a number "c" that is an element of (a, b) so that f''(c) = g''(c).

Any help/tips appreciated.

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    Consider the function $f'-g'$ and the mean value theorem or Rolle.2012-10-30

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Apply Rolle's theorem to $h(x) = f'(x)-g'(x)$