Solutions Calculus

Let f be a twice differentiable function on R with f” continuous on [0, 1] such that ∫_0^1{f(x)

Question: Let f be a twice differentiable function on R with f” continuous on [0, 1] such that

\[\int\limits_{0}^{1}{f\left( x \right)dx}=2\int\limits_{1/4}^{3/4}{f\left( x \right)dx}\]

Prove that there exists an xo that belongs to (0, 1) such that f”(xo) = 0.

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