The differential equation of the given equation

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

Solutions

Chapter 3.1, Problem 38E
To determine

To find:The differential equation of the given equation

Expert Solution

The equation is f(4)=124

Explanation of Solution

Given:

The function is

f(x)=1x

Concept used:

Definition of the differentiation:-Differentiation is the action of computing a derivative

The derivative of a function y=f(x) of a variable x is a measure of the rate at which the value y of the function changes with respect to x

Calculation:

The function

f(x)=1x...................(1)

The derivative of a function

y=f(x)y=f(x)=dydx

Differentiating the equation (1) with respect to x

dydx=ddx(1x)dydx=12x32f(x)=12x32.....................(2)

Replacing x by a in equation (2)

f(x)=12x32f(a)=12a32

Putting the given value a=4

f(4)=12(4)32f(4)=12(22)32f(4)=124

Draw the table

y=f(x)=3x2x3

Test one point in each of the region formed by the graph

If the point satisfies the function then shade the entire region to denote that every point in the region satisfies the function

 x−axis 0.11 0.25 3 3 y−axis 3.002 2 0 0.57

Have a homework question?

Subscribe to bartleby learn! Ask subject matter experts 30 homework questions each month. Plus, you’ll have access to millions of step-by-step textbook answers!