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 31E

To determine

To find the values of x and y .

Expert Solution

Answer to Problem 31E

The largest volume of x=12 ,and y=6 .

Explanation of Solution

Given equation 2x+2y=36.

Calculation:

2x+2y=36 , therefore, y=18−x and the volume of the cylinder is

V=π(x2π)2⋅y=π(x2π)2⋅(18−x)

Find the derivative of V ,

V=x24π2⋅(18−x)V′=2x4π2(18−x)+x24π2⋅(−1) =−3x2+36x4πV′=0=−3x2+36x4π−3x2+36x=036x=3x2 x=12

Plug in 12 for x in the perimeter equation to find y .

y=18−12 =6

Thus, the largest volume of x=12 ,and y=6 .

To determine

To find the values of x and y .

Expert Solution

Answer to Problem 31E

Thus, the largest volume of x=12 ,and y=6 .

Explanation of Solution

Given equation y=18−x.

Calculation:

From the problem y=18−x and the volume is,

V=πx2⋅y =πx2⋅(18−x)

Then one should maximize the function f(x)= x2⋅(18−x)

f′(x)= 2x⋅(18−x)−x2 with solution x=12,y=6

Thus, the largest volume of x=12 ,and y=6 .

Chapter 5.4, Problem 30E

Chapter 5.4, Problem 32E

Chapter 5 Solutions

Calculus: Graphical, Numerical, Algebraic

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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