Mathegoras

Calculus › Extrema and curve sketching › Bounds from derivatives

Smoothness of f from an integral

University · ●●○○○ 20 pts

Let ff be a continuous function and let g(x)=∫0xf(y)(y−x) dyg(x) = \int_0^x f(y)(y - x)\,dy. Suppose gg is three times continuously differentiable. What is the greatest integer nn such that ff must be nn times continuously differentiable?

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