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AP® Calculus AB-BC

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Higher Order Derivatives: Where $f^{ k }\left( x \right) =0$

APCALC-NUK1BS

Which of the following functions satisfies the condition $f^{ k }\left( x \right) =0$ for all $k\ge 5$?

I. $f\left( x \right) ={ x }^{ 3 }+4x+4$
II. $f\left( x \right) =-{ 3x }^{ 4 }+2{ x }^{ 3 }-6x+1$
III. $f\left( x \right) ={ 2x }^{ 5 }-3{ x }^{ 2 }+7$

A

I only.

B

II only.

C

I and II only.

D

I, II, and III.