A differentiable function is approximated by the polynomial Q(x)=4x^3-36x^2+108x-104

MATHEMATICS · Multi-part · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series

Problem

A differentiable function

h

is approximated by the polynomial

Q(x)=4x^3-36x^2+108x-104.

Assume

Q

is written in expanded form and arises from a Taylor polynomial of minimal degree. (a) Determine the center

x=a

of this polynomial representation and the degree

n

. (b) Use

Q

to approximate

h(5.2)

, showing all steps of your calculation.