For all twice differentiable functions f:R→R, with f(0)=f(1)=f'(0)=0 ,

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f''(x)=0, for some x∈(0,1)

f''(x)=0, at every point x∈(0,1)

f''(x)≠0 at every point x∈(0,1)

f''(0)=0

answer is A.

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Detailed Solution

f(0)=f(1)=0⇒f1(c)=0 for some c∈(0,1) Now f1(0)=f1(c)=0⇒f11(x)=0 for some x∈(0,c)

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