11. A rain gutter piece is to be made of aluminum sheets that are 20 inches wide and 15 inches long, by turning up the edges 90 °C. 20 in 15 in s X a. Write down an equation for the volume of the gutter piece as a function of x. b. What depth z will provide maximum volume (and hence allows the most water in the gutter)? Use derivatives! c. What is the maximum value? Now, assume that the aluminum sheets are a inches wide. d. Determine the maximal volume. (Your result will contain the parameter a.)

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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11. A rain gutter piece is to be made of aluminum sheets that are 20 inches wide and 15 inches long, by
turning up the edges 90 °C.
20 in
15 in
s
X
a. Write down an equation for the volume of the gutter piece as a function of a.
b. What depth z will provide maximum volume (and hence allows the most water in the gutter)?
Use derivatives!
c. What is the maximum value?
Now, assume that the aluminum sheets are a inches wide.
d. Determine the maximal volume. (Your result will contain the parameter a.)
Transcribed Image Text:11. A rain gutter piece is to be made of aluminum sheets that are 20 inches wide and 15 inches long, by turning up the edges 90 °C. 20 in 15 in s X a. Write down an equation for the volume of the gutter piece as a function of a. b. What depth z will provide maximum volume (and hence allows the most water in the gutter)? Use derivatives! c. What is the maximum value? Now, assume that the aluminum sheets are a inches wide. d. Determine the maximal volume. (Your result will contain the parameter a.)
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