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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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Try applying mean value theorem to $f'-g'$ in $[a,b]$. –  Manzano Oct 30 '12 at 22:28
    
Consider the function $f'-g'$ and the mean value theorem or Rolle. –  Hagen von Eitzen Oct 30 '12 at 22:29

1 Answer 1

up vote 2 down vote accepted

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

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