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.