A cubic polynomial is used to approximate near

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

Problem

A cubic polynomial

p(x)=1+x+Ax^{3}

is used to approximate

e^{x}

near

x=0

. Find the value of

A

that makes the third derivative of

p

equal to the third derivative of

e^{x}

x=0

Related theory

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

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