# Math Help - Differentiable function on an interval.

1. ## Differentiable function on an interval.

if a function f is differentiable on (0,1) and the derivative of f'(x) does not equal 1 for any x in (0,1), Why is it the case that for some y,z in (0,1) if f(y)=y and f(z)=z, then z=y?

2. ## Re: Differentiable function on an interval.

Do you mean $f'(x)\ne0$?

no, f'(x)≠1

4. ## Re: Differentiable function on an interval.

Okay, sorry, I initially misread...I would take a look at the mean value theorem.