   Chapter 2.9, Problem 4E

Chapter
Section
Textbook Problem

# 1–4 Find the linearization L ( x ) of the function at a. f ( x ) = 2 / x 2 − 5 ,  a=3

To determine

To find:

The linearization L(x) of the function at a = 3.

Explanation

1) Formula:

i. Lx=fa+f '(a)(x-a)

ii. Power rule combined with chain rule :

ddxf(x)n=nfxn-1.f'(x)

iii. Constant multiple rule:

ddxc.fx=c.ddxfx where c is constant.

iv. Difference rule:

ddxfx-gx=ddxfx-ddxg(x)

2) Given:

fx=2x2-5, a=3

3) Calculation:

Substitute x = a, to find f(a)

fa=2a2-5

Now substitute a = 3, in f(a)

f3=232-5=24=22=1

Differentiate f(x) with respect to x,

f'x=ddx2x2-5

By using power rule combined with chain rule and constant multiple rule,

f'x=-22(x2-5)x2-5

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