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**neeeeed helppppp for a question,,urgent!(not hw)**

Hi, I have been working on this question for some time,, but still couldn't solve it,,does anyone have an idea? thanks for helping!

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 some x in [0,1].

In more picturesque terms: A particle which travels a unit distance in a unit time, and starts and ends with velocity 0, has at some time an acceleration>=4

Hint:Prove that either f ' ' (x)>4 for some x in [0, 1/2] or f ' '(x)<-4 for some x in [1/2, 1].

and show that in fact we must have/ f ''(x)/ >4 for some x in [0,1]