# Prove Differentiable continuous function...

• Sep 17th 2012, 06:32 AM
kspkido
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..
• Sep 17th 2012, 06:41 AM
Plato
Re: Prove Differentiable continuous function...
Quote:

Originally Posted by 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 $[a,b]$ realizing that the slope of $y=x$ is $1$.