a. Answer the max value is 40 at x = 10 . Explanation Given information: The function is P ( x ) = 2 x + 200 x , 0 < x < ∞ . Calculation: to find the extreme value, differentiate the function because function has no end points, P ( x ) = 2 x + 200 x P ' ( x ) = 2 − 200 x 2 [differentiate and simplify] Now, equal the differentiation to zero, 2 − 200 x 2 = 0 2 x 2 = 200 [simplify] x = 10 [simplify] Substitute the value in the function, P ( x ) = 2 x + 200 x P ( 10 ) = 2 ( 10 ) + 200 10 [substitute x = 10 ] P ( 10 ) = 40 [simplify] Thus, the max value is 40 at x = 10 . b. To determine To find: the interpretation in terms of perimeter of the rectangle by the value occur in part (a). Answer The interpretation in terms of perimeter of the rectangle is 40 at x = 10 . Explanation Given information: The function is P ( x ) = 2 x + 200 x , 0 < x < ∞ . Calculation: from the part (a), the value is x = 10 and substitute the value of function, P ( x ) = 2 x + 200 x P ( x ) = 2 ( 100 x ) + 200 100 x [ x by 100 x ] P ( x ) = 200 x + 2 x [simplify] P ( 10 ) = 40 [substitute x = 2 and simplify] Thus, the max value is 40 at x = 10 .

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 5.1, Problem 44E

To determine

To find: the extreme value of function.

Expert Solution

Answer to Problem 44E

the max value is 40 at x=10 .

Explanation of Solution

Given information:

The function is P(x)=2x+200x, 0<x<∞ .

Calculation: to find the extreme value, differentiate the function because function has no end points,

P(x)=2x+200xP'(x)=2−200x2 [differentiate and simplify]

Now, equal the differentiation to zero,

2−200x2=02x2=200 [simplify]x=10 [simplify]

Substitute the value in the function,

P(x)=2x+200x P(10)=2(10)+20010 [substitute x=10]P(10)=40 [simplify]

Thus, the max value is 40 at x=10 .

To determine

To find: the interpretation in terms of perimeter of the rectangle by the value occur in part (a).

Expert Solution

Answer to Problem 44E

The interpretation in terms of perimeter of the rectangle is 40 at x=10 .

Explanation of Solution

Given information:

The function is P(x)=2x+200x, 0<x<∞ .

Calculation: from the part (a), the value is x=10 and substitute the value of function,

P(x)=2x+200xP(x)=2(100x)+200100x [x by 100x]P(x)=200x+2x [simplify]P(10)=40 [substitute x=2 and simplify]

Thus, the max value is 40 at x=10 .

Chapter 5.1, Problem 43E

Chapter 5.1, Problem 45E

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

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