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AP® Calculus AB-BC

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Interpreting a Second Derivative

APCALC-BKBSXO

If $f(t)$ is a continuous and twice-differentiable function that represents the height of a tree (in feet) at any time $t$ (in years), which statement best describes the meaning of $f^{\prime\prime}(2)=3$?

A

The rate that the height of the tree is growing is increasing at a rate of $3\text{ feet/year}$ per year at the beginning of the second year.

B

The height of the tree is increasing at a rate of $3\text{ feet/year}$ at the beginning of the second year.

C

The rate that the height of the tree is growing is increasing at a rate of $2\text{ feet/year}$ per year at the beginning of the third year.

D

The height of the tree is increasing at a rate of $2\text{ feet/year}$ at the beginning of the third year.

E

The tree is $3\text{ feet}$ tall at the beginning of the second year.