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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 $1\le f'(x)\le 3$, what is the largest possible value for $f(10)$?

A

$13$

B

$19$

C

$24$

D

$29$

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