Question involving differentiation

[holezch]

Homework Statement

Prove that if F is a twice differentiable function with F(0) = 0 and F(1) = 1 and F'(0) = F'(1) = 0, then |F''(x)| >= 4 for x in (0,1).



Hint: Prove that either F"(x) >= 4 for some x in (0,1/2) or else F"(x) <= -4 for some x in (1/2,1)


Then, show that we actually have |F"(x)| > 4.

Homework Equations

I suppose we'll be using the mean value theorem..

The Attempt at a Solution

No tangible idea as to where to start..

Thanks

 

[lanedance]

have you had a look at rolle's theorem?