Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)

4th Edition

ISBN: 9780133178579

Author: Ross L. Finney

Publisher: PEARSON

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Question

Chapter 5.4, Problem 1E

To determine

Find the Given sum of two non-negative numbers.

Expert Solution

Answer to Problem 1E

The maximum sum the numbers are (0,20) and sum is 400 for minimum sum the numbers are (10,10) and sum is 200.

Explanation of Solution

Calculation: Given sum of two non-negative numbers is 20 .

Let the numbers are x and y 0<x<20

x+y=20y=20−x

Let the sum of squares of x and y be S

S=x2+y2 =x2+(20−x)2 =x2+400+x2−40x =2x2+400−40x

For any function f(x) the condition of minimum and maximum is obtained by find f(x)′=0, critical points and end points.

At critical points if f(x)′<0, then the critical point gives the maxima of the function f(x)

At critical points if f(x)′>0, then the critical point gives the minima of the function f(x)

f(x)=S=2x2+400−40xf′(x)=4x−40

Solve it graphically its critical points and end points occur at x=10,x=0,x=20

x=10,,y=20S=2x2+400−40x =400For x=20,,y=0S=2x2+400−40x =2(400)+400−40(20) =800+400−800 =400For x=20,,y=0S=2x2+400−40x =2(100)+400−40(10) =200+400−400 =200

Graphical support:

Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy), Chapter 5.4, Problem 1E , additional homework tip 1

Thus , The maximum sum the numbers are (0,20) and sum is 400 for minimum sum the numbers are (10,10) and sum is 200.

To determine

Find the Given sum of two non-negative numbers.

Expert Solution

Answer to Problem 1E

The maximum sum the numbers are (794,14) and sum is 814 for minimum sum the numbers are (0,20) and sum is 20.

Explanation of Solution

Calculation:Given sum of two non negative numbers is 20 .

The sum of one number and the square root of other number be f(x)

f(x)=x+20−xf′(x)=1−12(20−x)

Solve it graphically its critical points and end points occur at x=794,x=0,x=20

x=0,,y=20

f(x)=x+20−x =20 =4.47

x=20,,y=0

f(x)=x+20−x =20

x=794,y=14

f(x)=x+20−x =814

Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy), Chapter 5.4, Problem 1E , additional homework tip 2

Thus , The maximum sum the numbers are (794,14) and sum is 814 for minimum sum the numbers are (0,20) and sum is 20.

Chapter 5.4, Problem 10QR

Chapter 5.4, Problem 2E

Chapter 5 Solutions

Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)

Ch. 5.1 - Prob. 1QR Ch. 5.1 - Prob. 2QR Ch. 5.1 - Prob. 3QR Ch. 5.1 - Prob. 4QR Ch. 5.1 - Prob. 5QR Ch. 5.1 - Prob. 6QR Ch. 5.1 - Prob. 7QR Ch. 5.1 - Prob. 8QR Ch. 5.1 - Prob. 9QR Ch. 5.1 - Prob. 10QR

Ch. 5.1 - Prob. 11QR Ch. 5.1 - Prob. 12QR Ch. 5.1 - Prob. 1E Ch. 5.1 - Prob. 2E Ch. 5.1 - Prob. 3E Ch. 5.1 - Prob. 4E Ch. 5.1 - Prob. 5E Ch. 5.1 - Prob. 6E Ch. 5.1 - Prob. 7E Ch. 5.1 - Prob. 8E Ch. 5.1 - Prob. 9E Ch. 5.1 - Prob. 10E Ch. 5.1 - Prob. 11E Ch. 5.1 - Prob. 12E Ch. 5.1 - Prob. 13E Ch. 5.1 - Prob. 14E Ch. 5.1 - Prob. 15E Ch. 5.1 - Prob. 16E Ch. 5.1 - Prob. 17E Ch. 5.1 - Prob. 18E Ch. 5.1 - Prob. 19E Ch. 5.1 - Prob. 20E Ch. 5.1 - Prob. 21E Ch. 5.1 - Prob. 22E Ch. 5.1 - Prob. 23E Ch. 5.1 - Prob. 24E Ch. 5.1 - Prob. 25E Ch. 5.1 - Prob. 26E Ch. 5.1 - Prob. 27E Ch. 5.1 - Prob. 28E Ch. 5.1 - Prob. 29E Ch. 5.1 - Prob. 30E Ch. 5.1 - Prob. 31E Ch. 5.1 - Prob. 32E Ch. 5.1 - Prob. 33E Ch. 5.1 - Prob. 34E Ch. 5.1 - Prob. 35E Ch. 5.1 - Prob. 36E Ch. 5.1 - Prob. 37E Ch. 5.1 - Prob. 38E Ch. 5.1 - Prob. 39E Ch. 5.1 - Prob. 40E Ch. 5.1 - Prob. 41E Ch. 5.1 - Prob. 42E Ch. 5.1 - Prob. 43E Ch. 5.1 - Prob. 44E Ch. 5.1 - Prob. 45E Ch. 5.1 - Prob. 46E Ch. 5.1 - Prob. 47E Ch. 5.1 - Prob. 48E Ch. 5.1 - 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