For the polynomial

MATHEMATICS · Single correct · AP · Calculus AB · Differentiation: Composite, Implicit, and Inverse Functions · Differentiation: Composite, Implicit, and Inverse Functions

Problem

For the polynomial

f(x)=4x^3-6x

, identify the smallest positive integer

k

for which

f^{(k)}(x)=0

for all

x\in\mathbb{R}

. (a)

3

(b)

5

(c)

4

(d)

2

Related theory

Higher-Order Derivatives
Advanced Differentiation
Second order derivatives
Continuity and Differentiability

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