   Chapter 9.8, Problem 32E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# In Problems 31 and 32, do the following for each function f ( x ) . ( a )     Find  f ( x )  and  f " ( x ) . ( b )    Graph  f ( x ) ,   f ' ( x ) ,  and  f ” ( x )  with a graphing utility . ( c )     Identify x-values where  f " ( x ) =   0 ,    f " ( x )   >   0 , and f " ( x )   < 0. ( d )    Identify  x -values where  f ' ( x )  has a maximum point or a minimum point, where  f ' ( x )  is increasing, and where   f ' ( x )  is decreasing . ( e )     When  f ( x )  has a maximum point, is  f ” ( x ) >   0  or  f " ( x )   < 0 ? ( f )     When  f ( x )  has a minimum point, is  f " ( x ) >   0  or  f " ( x )   < 0 ?   f ( x ) = 2 + 3 x − x 3

(a)

To determine

To calculate: The first derivative and second derivative of the function f(x)=2+3xx3.

Explanation

Given Information:

The provided function is,

f(x)=2+3xx3

Formula used:

If the function f(x)=xn, where n is a real number then the derivate of function is f(x)=nxn1 known as a power rule x rule.

If the function f(x)=cu(x), where c is a constant and the function u(x) is a differentiable function of x then derivative of function is f(x)=cu(x) known as coefficient rule.

Calculation:

Consider the provided function,

f(x)=2+3xx3

Now, use the power rule and coefficient of derivatives,

The function f(x)=xn, where n is a real number then the derivate of function is f(x)=nxn1

(b)

To determine

To graph: The functions f(x)=2+3xx3, f(x)=33x2 and f(x)=6x.

(c)

To determine

The values of x where f(x)=0, f(x)>0 and f(x)<0 if f(x)=2+3xx3.

(d)

To determine

The values of x where f(x) has a maximum point, minimum point, increasing and decreasing.

(e)

To determine

Whether the second derivate of function f(x)<0 or f(x)>0 if f(x) has a maximum point.

(f)

To determine

Whether the second derivate of function f(x)<0 or f(x)>0 if f(x) has a minimum point.

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

#### Solve the equations in Exercises 126. (x21)2(x+2)3(x21)3(x+2)2=0

Finite Mathematics and Applied Calculus (MindTap Course List)

#### In Exercises 49-62, find the indicated limit, if it exists. 62. limx24x22x2+x3

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

#### The solution to y = y2 with y(1)=13 is: a) y=1x+2 b) y=lnx+13 c) y=12x216 d) y=12x16

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th 