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AP® Calculus AB-BC

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Using Mean Value Theorem with a Table of Values

APCALC-UE1SQ2

Given the table of values of a continuous, differentiable function $f(x)=xsin(x)+x$:

x f(x)
-2 -0.181
-1 -0.158
1 1.841
2 3.818

$\ $
Which statement is correct based on the Mean Value Theorem?

A

The point $(0,0)$ must be on the curve.

B

A value of $x=c$ exists on $[-2,2]$ such that $f'(c)=0.674$.

C

A value of $x=c$ exists on $[-2,2]$ such that $f(c)=1$.

D

A value of $x=c$ exists on $[-2,2]$ such that $f'(c)=1$.