   Chapter 2.9, Problem 1E

Chapter
Section
Textbook Problem

# 1–4 Find the linearization L ( x ) of the function at a. f ( x ) = x 3 − x 2 + 3 ,  a=-2

To determine

To find:

The linearization L(x) of the function at a = -2

Solution:

Lx=16x+23

Explanation

1) Formula:

i. Lx=fa+f '(a)(x-a)

ii.

ddxxn=nxn-1

2) Given:

fx=x3-x2+3, a=-2

3) Calculation:

Substitute x = a, to find f (a)

fa=a3-a2+3

Now substitute a = -2, in f (a)

f-2=(-2)3--22+3= -8-4+3=-9

By applying the formula,

ddxxn=nx<

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