Prove Differentiable continuous function...

**Let function ***f *be continuous on [a, b] and differentiable on (a,b) with f(a)=a and f(b)=b. Prove that there is a point in the graph of between (a, f(a)) and (b, f(b)) at which the tangent line is parallel to y=x...

Thank you very much for your help.... wew please show it to me in simpler step by step method so i could follow it.. thank you..

Re: Prove Differentiable continuous function...

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**kspkido** **Let function ***f *be continuous on [a, b] and differentiable on (a,b) with f(a)=a and f(b)=b. Prove that there is a point in the graph of between (a, f(a)) and (b, f(b)) at which the tangent line is parallel to y=x...

Apply the mean value theorem of $\displaystyle [a,b]$ realizing that the slope of $\displaystyle y=x$ is $\displaystyle 1$.