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AP® Calculus AB-BC

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Lagrange Error Using a Table

APCALC-ZSGLVD
x f'(x) f"(x) f'''(x)
0 -1 2 -6
1 -1/2 1/4 3/8

$$\quad$$
Let $f(x)$ be a decreasing function with values for the first, second, and third derivatives evaluated at $x = 0$ and $x = 1$ given in the table shown above.

Given that the third derivative is strictly increasing on the interval $[0,1]$, if a second degree Taylor Polynomial centered at $x = 0$ is used to approximate $f(1)$, find the estimated error using Lagrange error bound.

A

$\cfrac{1}{16}$

B

$\cfrac{1}{6}$

C

$\cfrac{3}{8}$

D

$1$