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Math Help - Prove Differentiable continuous function...

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    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..
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    Re: Prove Differentiable continuous function...

    Quote Originally Posted by kspkido View Post
    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 [a,b] realizing that the slope of y=x is 1.
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