   Chapter 16.1, Problem 30E

Chapter
Section
Textbook Problem

Match the functions f with the plots of their gradient vector fields labeled I-IV. Give reasons for your choices.30. f(x, y) = x(x + y) To determine

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

Explanation

Given data:

The function is f(x,y)=x(x+y).

Formula used:

The gradient vector field of two dimensional vector is given by,

f(x,y)=fxi+fyj

Calculation:

Find the gradient vector field of f(x,y)=x(x+y), by the use of above mentioned formula as,

f(x,y)=x(x(x+y))i+y(x(x+y))j=x(x2+xy)i+y(x2+xy)j (1)

Differentiate the term x2+xy with respect to x as,

x(x2+xy)=x(x2)+x(xy)=2x+y

Differentiate the term x2+xy with respect to y

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