   Chapter 4.1, Problem 51E ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# Find the absolute maximum and absolute minimum values of f on the given interval.f(x) = 3x4 − 4x3 − 12x2 + 1, [−2, 3]

To determine

To find: The absolute maximum and absolute minimum of the given function.

Explanation

Given:

The function f(x)=3x44x312x2+1 in the interval [2,3] .

Power Rule:

If n is positive integer, then ddx(xn)=nxn1 (1)

Calculation:

Obtain the first derivative of the given function.

f(x)=ddx(3x44x312x2+1)=ddx(3x4)ddx(4x3)12ddx(x2)+ddx(1)

Apply the power rule as shown in equation (1),

f(x)=3(4x41)4(3x31)12(2x21)+0=12x312x224x=12x(x2x2)=12x(x+1)(x2)

Set f(x)=0 and obtain the critical numbers.

12x(x+1)(x2)=0x=0,x=1,x=2

Thus, the critical points are 1,0 and 2 , which lies in the given interval [2,3] .

Apply the extreme values of the given interval and the critical number values in f(x)

### 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

#### Sketch the graphs of the equations in Exercises 512. xy=2x3+1

Finite Mathematics and Applied Calculus (MindTap Course List)

#### What are the two requirements for a random sample?

Statistics for The Behavioral Sciences (MindTap Course List)

#### In problems 45-62, perform the indicated operations and simplify. 46.

Mathematical Applications for the Management, Life, and Social Sciences

#### The area of the shaded region is given by:

Study Guide for Stewart's Multivariable Calculus, 8th

#### The general solution to (for x, y > 0) is: a) y = ln x + C b) c) y = ln(ln x + C) d)

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

#### Explain the distinction between science and pseudoscience.

Research Methods for the Behavioral Sciences (MindTap Course List) 