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

4th Edition

ISBN: 9780133178579

Author: Ross L. Finney

Publisher: PEARSON

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.

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Question

Chapter 5.4, Problem 8E

To determine

Prove the maximum area of the dimensions are a=b

Expert Solution & Answer

Answer to Problem 8E

The maximum area of the dimensions are a=b is (14.14,14.14) and area is 100units

Explanation of Solution

Given information: Given the length of the line is 20 units with coordinates (a,0)(0,b)

Calculation:

Let the sides length of the triangle is a,b(0<a<20)

(a2+b2)=202b2=400−a2b=400−a2

Let the area of the triangle be ,

A=12(a)(b)=12(a)(400−a2)

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

Critical points and end points

A=12(a)(400−a2)dAda=12(400−a2)+(a)2(225−x2)(−2a) =12(400−a2)−(a2)2(400−a2) =(400−2a2)2(400−a2) =(200−a2)(400−a2)

Critical points occur at

A′=0(200−a2)(400−a2)=0200−a2=0a=±200

Consider a=200 since 0<a<20 ,solve it graphically, it has critical point occur at a=200

Here dAda>0 for 0<a<200 and dAda<0for200<a<20 this corresponds to maximum area.

For

a=200 b=(400−a2) =400−200 =200≈14.14a=bA=12(200)(200) =100

Graphical support:

Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy), Chapter 5.4, Problem 8E

Thus, the maximum area of the dimensionsare a=b is (14.14,14.14) and area is 100units

Chapter 5.4, Problem 7E

Chapter 5.4, Problem 9E

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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Prove the maximum area of the dimensions are a = b

Concept explainers

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Prove the maximum area of the dimensions are a=b

Answer to Problem 8E

Explanation of Solution

Chapter 5 Solutions

Additional Math Textbook Solutions