To determine To calculate: The absolute extrema of provided function f ( x ) = 1 x 2 + 1 on the given interval. Explanation Given: The provided function is f ( x ) = 1 x 2 + 1 ; [ − 1 , 1 ] . Formula used: The property of derivative as; d d x ( x n ) = n x n − 1 And Extreme value theorem If a function f ( x ) is continuous on a closed interval [ a , b ] and has only one critical number in the interval [ a , b ] , say, x = c . Then, f ( x ) has both absolute maxima and absolute minima in the given interval occurring either at an endpoint of [ a , b ] or at the critical number x = c . Calculation: According to the extreme-value theorem, we need consider only the critical numbers of f and the endpoints, -1 and 1, of the interval. Begin by finding the derivative and determining the critical numbers: f ' ( x ) = ( − 1 2 ) ( x 2 + 1 ) − 1 2 − 1 ⋅ d d x [ x 2 + 1

12th Edition

ISBN: 8220106844557

Author: MULLINS

Publisher: PEARSON

See similar textbooks

Concept explainers

Minimization

In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in ter…

Maxima and Minima

The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.

Derivatives

A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which …

Concavity

In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the …

Videos

Question

Chapter 12.3, Problem 17E

To determine

To calculate: The absolute extrema of provided function f (x) =1x2+1 on the given interval.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 12.3, Problem 16E

Chapter 12.3, Problem 18E

Students have asked these similar questions

Use the method of disks to find the volume of the solid that is obtained when the region under the curve y = over the interval [4,17] is rotated about the x-axis.

search P(QP) Q 1.-P:PR 2.-QP:PR 3. Q:MT 1, 2 4. Q:DNE 3 Submit 4.5 P. (QP) Q 1. P: PR 2. Q-P PR 3. -Q:AS 4. -P:MP 2, 3 5. Submit 17 A Previous Chapter Next Chapter

1. Find the area of the region enclosed between the curves y = x and y = x. Sketch the region.

Chapter 12 Solutions

EBK MATHEMATICS WITH APPLICATIONS IN TH

Ch. 12.1 - Checkpoint 1 For what values of x is the function...Ch. 12.1 - Checkpoint 2 Find all intervals on which is...Ch. 12.1 - Checkpoint 3 Identity the x-values of all points...Ch. 12.1 - Checkpoint 4 Find the critical numbers for each of...Ch. 12.1 - Prob. 5CP Ch. 12.1 - Prob. 6CP Ch. 12.1 - Checkpoint 7 Find the locations of the local...Ch. 12.1 - Prob. 8CP Ch. 12.1 - Checkpoint 9 If a sales function is given by...Ch. 12.1 - Prob. 1E

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.