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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Do you mean $\displaystyle f'(x)\ne0$?
no, f'(x)≠1
Okay, sorry, I initially misread...I would take a look at the mean value theorem.
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