AP® Calculus AB-BC

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Difficult

Mean Value Theorem to find the Smallest $f(a)$ Given $f(b)$

APCALC-R@1BVO

You are given a function $f(x)$ that is continuous on the closed interval $[-1,4]$ and differentiable on the open interval $(-1,4)$.

If $f(4)=10$ and the average rate of change is bounded between $-4$ and $3$, that is: $-4\le f'(x)\le 3$, what is the smallest possible value for $f(-1)$?

A

$-5$

B

$-15$

C

$-25$

D

$30$