Thread: 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..

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 realizing that the slope of is .