A differentiable function is modeled near a point by the polynomial…

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

Problem

A differentiable function

p

is modeled near a point by the polynomial

S(x)=3x^2-12x+13+5(x^2-4x+4)^2.

Assume

S

is the Taylor polynomial of least possible degree that matches

p

at the appropriate point. (a) Determine the center

x=a

of this polynomial representation and the degree

n

. (b) Rewrite

S(x)

explicitly as a polynomial in powers of

(x-a)

to verify your answers from part (a). (c) Use

S

to approximate

p(1.8)

. (d) Compute

S'(a)

and explain what this value estimates about

p