A real function f is defined for 0≤x≤1, with its first derivative f′ defined for 0≤x≤1 and its second derivative f′′ defined for 0<x<1. Prove that if f(0)=f′(0)=f′(1)=f(1)−1=0, then there exists a number 0<y<1 such that ∣f′′(y)∣≥4. calculusderivativefunctioninequalitiesintegrationreal analysisreal analysis unsolved