Thread: Tricky 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?

Originally Posted by joeyjoejoe

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?

Since F is continuous on [a, b] it is integrable there. Let and apply Rolle's theorem to .

Let

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