OptimizationThe sum of two nonnegative numbers is 36. Find

Thomas' Calculus: Early Transcendentals | 13th Edition | ISBN: 9780321884077 | Authors: George B. Thomas Jr., Maurice D. Weir, Joel R. Hass

Problem 85PE Chapter 4

Thomas' Calculus: Early Transcendentals | 13th Edition

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Thomas' Calculus: Early Transcendentals | 13th Edition | ISBN: 9780321884077 | Authors: George B. Thomas Jr., Maurice D. Weir, Joel R. Hass

Thomas' Calculus: Early Transcendentals | 13th Edition

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Problem 85PE

Optimization

The sum of two nonnegative numbers is 36. Find the numbers if

a. the difference of their square roots is to be as large as possible.

b. the sum of their square roots is to be as large as possible.

Step-by-Step Solution:

Step 1 of 6:

a)In this problem, we need to find the numbers if the difference of their square roots is to be as large as possible.

Step 2 of 6:

Given:The sum of two nonnegative numbers is 36.

Let us consider, x and y are two nonnegative numbers.

Given:

Difference of their square roots is maximum means

 , where

Now, differentiate on both sides we get.

       

Therefore, does not exist at  and .

Step 3 of 6:

Clearly, f(x) has critical points at 0,18, and 36.

At ,  

At ,  

At ,  

Hence, the maximum value attains at

Another number is:

Therefore, the numbers are “0 and 36”.

Step 4 of 6

Chapter 4, Problem 85PE is Solved
Step 5 of 6

Textbook: Thomas' Calculus: Early Transcendentals
Edition: 13th
Author: George B. Thomas Jr., Maurice D. Weir, Joel R. Hass
ISBN: 9780321884077

Since the solution to 85PE from 4 chapter was answered, more than 224 students have viewed the full step-by-step answer. The answer to “OptimizationThe sum of two nonnegative numbers is 36. Find the numbers ifa. the difference of their square roots is to be as large as possible.b. the sum of their square roots is to be as large as possible.” is broken down into a number of easy to follow steps, and 38 words. The full step-by-step solution to problem: 85PE from chapter: 4 was answered by Sieva Kozinsky, our top Calculus solution expert on 08/01/17, 02:37PM. Thomas' Calculus: Early Transcendentals was written by Sieva Kozinsky and is associated to the ISBN: 9780321884077. This textbook survival guide was created for the textbook: Thomas' Calculus: Early Transcendentals , edition: 13th. This full solution covers the following key subjects: sum, square, large, roots, Numbers. This expansive textbook survival guide covers 138 chapters, and 9198 solutions.

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