# Differentiation problem

1. Jan 1, 2009

### johnson12

Let f be continuous on [0,1] and differentiable on (0,1) such that f(0)=f(1), prove that there exist a 0 < c < 1 such that f$$\acute{}$$(1-c) = -f$$\acute{}$$(c).

thanks for any suggestions.

2. Jan 1, 2009

### NoMoreExams

Just from the givens it made me think of MVT...

3. Jan 1, 2009

### johnson12

That was my first impression but it seems to be a little trickier than that.

4. Jan 1, 2009

### Dick

It's a little more complicated, but not much. Define g(x)=f(x)+f(1-x). g(0)=g(1), right?