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**Challanging Problem " It is nessecary to solve quicly"**

I have a problem :

A car moves along the real line from x = 0 at t = 0 to x = 1 at t = 1, with

differentiable position function x(t) and differentiable velocity function v(t) = x’(t).

The car

begins and ends the trip at a standstill; that is v = 0 at both the beginning and the end of

the trip. Let L be the maximum velocity attained during the trip. Prove that at some time

between the beginning and end of the trip, l v’ l > L^2/(L-1).

Can you verify that L > 1 ?

Thankx