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AP® Calculus AB-BC

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Approximate Derivative Value, Given a Table of Data

APCALC-GC3O14

Consider a differentiable function, $g(x)$, for which some of its values are given below.

$x$ 2.99970 2.99980 2.99990 3.00000 3.00010 3.00020 3.00030
$g(x)\quad $ 2.15315 2.15548 2.15782 2.16016 2.16250 2.16345 2.16576



Based on the data, what is the approximate value of $g'(3)$?

A

$0.8376$

B

$23.4$

C

$2.16016$

D

$0.00468$