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AP® Calculus AB-BC

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Calculus Theorems from a Table

APCALC-SLMEYG
x 1 2 3 4 5
f(x) 10 6 -1 -2 10

$ f(x)$ is a differentiable function and selected values are given in the table above. Which of the following statements could be false?

A

$ f(x)=0$ at some point on the interval $[1,5]$.

B

$ f^\prime(x)=0$ at some point on the interval $(1,5)$.

C

$f(4)$ is a relative minimum.

D

$f(x)=7$ at some point on the interval $[1,5]$

E

$f^\prime(x)=-7$ at some point on the interval $(1,5)$.