   Chapter 14, Problem 8RCC

Chapter
Section
Textbook Problem

Define the linearization of f at (a, b). What is the corresponding linear approximation? What is the geometric interpretation of the linear approximation?

To determine

To define: The linearization of the function f at (a,b) and the corresponding linear approximation; also the geometric interpretation of the linear approximation at the point (a,b) .

Explanation

Consider the function f(x,y) .

The linearization of the function f(x,y) at the point (a,b) defined as,

L(x,y)=f(a,b)+fx(a,b)(xa)+fy(a,b)(yb) where fx(a,b) is a partial differential of x at the point (a,b) and fy(a,b) is a partial differential of y at the point (a,b)

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