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Calculus › Extrema and curve sketching › Bounds from derivatives

Smallest value from derivative bounds

High school · ●●○○○ 20 pts

Given that f(1)=3f(1) = 3 and 2≤f′(x)≤32 \leq f'(x) \leq 3 for all xx, what is the smallest possible value of f(4)f(4)?

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mean value theoremlinear approximation