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# Mean Value Theorem to Find the Minimum $f(b)$ Given $f(a)$

APCALC-19ZFMU

You are given a function $f(x)$ that is continuous on the closed interval $[2,10]$ and differentiable on the open interval $(2,10)$.

If $f(2)=5$ and the average rate of change is bounded between $-1$ and $3$, that is: $-1\le f'(x)\le 3$, what is the smallest possible value for $f(10)$?

A

$-13$

B

$-8$

C

$-3$

D

$29$