Linearization

The linearization of function y=f(x) near the value x=a is given by:

• L(x) = f(a) + f'(a) (x - a)

• L(a) = f(x) + f'(x) (x - a)

• L(x) = f'(a) + f(a) (x - a)

• L(a) = f'(x) + f(x) (x - a)

Use linearization to approximate 2.04³

• 212 / 25

• 53 / 5

• 106 / 15

• 477 / 50

• 4.6

• 4.7

• 4.8

• 4.9

What is the linearization function L(x) for f(x) = sin(x) for values of x near 0?

• L(x) = x

• L(x) = x + 1

• L(x) = sin(x) + x cos(x)

• L(x) = cos (x) (x - 0)

Use a linear approximation at x = 2 to estimate f(2.5).

• 10.5

• 11

• 11.5

• 12

Given f (x) = 3x² , will linear approximations to f overestimate or underestimate the actual function values?

• overestimate

• underestimate

Let f(x) = x³.  L(x) is the linearization of f(x) centered at x = 1.  Calculate df if ∆x = 0.1. 

• 0.1

• 3

• 0.3

• 1.3

Let f(x) = x³ and L(x) be the linearization of f(x) centered at x = 1. Calculate the approximation error when ∆x = 0.1. 

• 0.1

• 0.01

• 0.331

• 0.031

Which of these is the linear approximation to f centered at x = 1?

• y = 12x - 1

• y = 6x + 5

• y = 12x - 8

• y = 12x - 16

f(4) = 1
f'(4) = 3
Using a linear approximation centered at 4, f(4.5) ≈

• 5/2

• 3/2

• 4/3

• 7/3