Suppose that f is continuous and differentiable on [a,b], f(a) = f(b) = 0. Show that for every real number there is a real number c [a,b] such that f'(c) = f(c).

Tried to use MVT (and Rolle's) to no avail. Any suggestions?

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- June 5th 2009, 08:22 AMjoeyjoejoeTricky Advanced Calc Problem
Suppose that f is continuous and differentiable on [a,b], f(a) = f(b) = 0. Show that for every real number there is a real number c [a,b] such that f'(c) = f(c).

Tried to use MVT (and Rolle's) to no avail. Any suggestions? - June 5th 2009, 09:27 AMHallsofIvy
- June 11th 2009, 10:54 AMpankaj
Let

g(a)=g(b)=0.Now use Rolle's Theorem