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 34E
To determine

To find:The differential equation of the given equation

Expert Solution

The equation is f(x)=15x460x2+50

Explanation of Solution

Given:

The function is

f(x)=3x520x3+50x

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)=3x520x3+50x...................(1)

The derivative of a function

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

Differentiating the equation (1) with respect to x

dydx=ddx(3x520x3+50x)dydx=15x460x2+50f(x)=15x460x2+50

Draw the table

y=f(x)=3x520x3+50x

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 0 −0.04 0.1 y−axis 0 1 −1.99 4.9

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