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2 problems match “differentiability”. Clear

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1. Smoothness of f from an integral ●●○○○ 20 ptsLet $f$ be a continuous function and let $g(x) = \int_0^x f(y)(y - x)\,dy$. Suppose $g$ is three times continuously differentiable. What is the greatest integer $n$ such that $f$ must be $n$ times continuously differentiable?
2. Making a piecewise function differentiable at a join ●●○○○ 20 ptsLet $f(x)=ax+b$ for $x\le 2$ and $f(x)=2-x^2$ for $x>2$. Find $a$ and $b$ so that $f$ is differentiable at $x=2$.