Lagrange's mean value theorem
The Attempt at a Solution
There exists c belonging to (0,1) which satisfies f'(c) = f(1)-f(0)/1 = -f(0)
But this gets me nowhere close to the options... :(
But your h(x) had solved the problem. What was the error??edit
Sorry the post I made contained an error. I'm not quite sure how to fix it yet but basically what I think you need to do is find a function h(x) and define it in terms of some linear combination of f(x), f(0), f(1) so that it equals zero at the end points and then apply Rolle's Theorem.