Find the linear approximation of f(x)=√x when x = -27.

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question
Find the linear approximation of f(x)=√x when x = -27.
O
O
G
a.) L(x) = -27-3(x-27)
b.) L(x) = -3+ (x+27)
27
c.)
L(x) = -27+ 12/17 (x+27)
d.) L(x) = -3-3(x-27)
Transcribed Image Text:Find the linear approximation of f(x)=√x when x = -27. O O G a.) L(x) = -27-3(x-27) b.) L(x) = -3+ (x+27) 27 c.) L(x) = -27+ 12/17 (x+27) d.) L(x) = -3-3(x-27)
Expert Solution
Step 1 Linear approximation.

Linear approximation is an approximation of a general function using a linear function. It is useful when it is difficult to find the value of a function at a particular point.

The linear approximation formula is as follows:

Lx=fa+f'ax-a

where,

  • Lx is the linear approximation of fx at x=a.
  • f'a is the derivative of fx at x=a.
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