Rolle's Theorem Problem with f(a)=f(b)=0: Finding f'(c)=f(c)/c on [a,b]

[xXPhoenixFireXx]

Anyway, I've come across this problem that I can't figure out. It looks set up as a Rolle's Thm problem, but it just doesn't work out...

Let f be a continuous function on [a,b] and differentiable on (a,b) for some a,b > 0. Suppose f(a) = f(b) = 0.

Show that f'(c)=f(c)/c for some c between a and b.

The thing is this is next to straightforward problems like the integral of xsinx and |3-2x|>1. Am I just missing something?

I mean, I've spent about 3 hours looking for a similar problem/theorem in my Calc book; even just a pointer from someone who knows the answer would be great.

 

[0rthodontist]

Use Rolle's theorem on g(x) = f(x)/x

 

[xXPhoenixFireXx]

*smacks self hard*

I can't believe I missed that, thanks.