Calculus: Graphical, Numerical, Algebraic

3rd Edition

ISBN: 9780133688399

Author: Finney, Ross L.

Publisher: Pearson/Prentice Hall

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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: Graphical, Numerical, Algebraic, 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: Graphical, Numerical, Algebraic, 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: Graphical, Numerical, Algebraic

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