# The differentiation of the given function of the interval ### 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 48E
To determine

## To find:The differentiation of the given function of the interval

Expert Solution

The function of interval is (53,1)

### Explanation of Solution

Given:

The function is

f(x)=x34x2+5x

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)=x34x2+5x...................(1)

The derivative of a function

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

Differentiating the equation (1) with respect to x

dydx=ddx(x34x2+5x)f(x)=3x28x+5

The derivative is zero

f(x)=03x28x+5=03x23x5x+5=03x(x1)5(x1)=0(3x5)(x1)=0x=53,1

The function of interval is (53,1)

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