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?

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- Dec 7th 2012, 06:58 PMAquameatwadDifferentiable 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?

- Dec 7th 2012, 07:28 PMMarkFLRe: Differentiable function on an interval.
Do you mean $\displaystyle f'(x)\ne0$?

- Dec 7th 2012, 07:30 PMAquameatwadRe: Differentiable function on an interval.
no, f'(x)≠1

- Dec 7th 2012, 07:49 PMMarkFLRe: Differentiable function on an interval.
Okay, sorry, I initially misread...I would take a look at the mean value theorem.