   Chapter 16.1, Problem 29E

Chapter
Section
Textbook Problem

Match the functions f with the plots of their gradient vector fields labeled I-IV. Give reasons for your choices.29. f(x, y) = x2 + y2 To determine

To match: The function f(x,y)=x2+y2 with the plots labelled as I-IV.

Explanation

Given data:

f(x,y)=x2+y2

Formula used:

Write the expression for gradient vector field of two dimensional vector.

f(x,y)=fxi+fyj (1)

Write the required differentiation formulae with respect to x as follows.

x(x2)=2xx(y2)=0

Write the required differentiation formulae with respect to y as follows.

y(x2)=0y(y2)=2y

Differentiate the term x2+y2 with respect to x .

x(x2+y2)=x(x2)+x(y2)=2x+0=2x

Differentiate the term x2+y2 with respect to y

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