   Chapter 6.1, Problem 62E

Chapter
Section
Textbook Problem

Slope Field In Exercises 61–64, (a) sketch the slope field for the differential equation, (b) use theslope field to sketch the solution that passes through the given point, and (c) discuss the graph ofthe solution as and Use a graphing utility to verify your results. To print a blank graph, go toMathGraphs.com. y ′ = 1 3 x 2 − 1 2 x , ( 1 , 1 )

a)

To determine

To Graph: The slope field for the given differential equation.

Explanation

Given: y=13x212x, (1,1)

Graph:

We start by making a table showing the slopes at several points. The table shown is a small

sample. The slopes at many other points should be calculated to get a representative slope field.

 x -2 -2 -1 -1 0 0 1 1 2 2 y -1 1 -1 1 -1 1 -1 1 -1 1 y′=13x2−12x 2

b)

To determine

To Graph: The slope field to sketch the solution that passes through the given point.

c)

To determine
The graph of the solution as x and x.

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