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2 problems match “mean value theorem”. Clear

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1. Smallest value from derivative bounds ●●○○○ 20 ptsGiven that $f(1) = 3$ and $2 \leq f'(x) \leq 3$ for all $x$, what is the smallest possible value of $f(4)$?
2. Points where f equals its average value ●●○○○ 20 ptsLet $f(x) = (x-2)^2$. Find all values of $c$ such that $f(c)$ equals the average value of $f$ over the closed interval $[-1, 5]$. Round each answer to two decimal places.