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Homework Statement
Homework Equations
Lagrange's mean value theorem
The Attempt at a Solution
Applying LMVT,
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.
Yah... Was just thinking the same and was about to post it... :PActually a relatively simple function works lol. Sorry for all this confusion:
[tex]
h(x) = xf(x)[/tex]
There exists a c in (0, 1) such that [tex]
0 = cf'(c) + f(c)[/tex]
by Rolle's Theorem.