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A box with no top is made from a rectangle with dimensions a = 15 inches by b= 11 inches by cutting a square of side x at each corner and turning up the sides (see the figure). Determine the value of that results in a box with the maximum volume. Following the steps to solve the problem. (1) Express the volume V as a function of x: V = (2) Determine the domain of the function V of x (use interval notation): (3) Find the derivative of the function V: V' =

A box with no top is made from a rectangle with dimensions a = 15 inches by b= 11 inches by cutting a square of side x at each corner and turning up the sides (see the figure). Determine the value of that results in a box with the maximum volume. Following the steps to solve the problem. (1) Express the volume V as a function of x: V = (2) Determine the domain of the function V of x (use interval notation): (3) Find the derivative of the function V: V' =

Calculus: Early Transcendentals
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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A box with no top is made from a rectangle with dimensions a = 15 inches by b= 11 inches by cutting a square of side x at each corner and turning up the sides (see the figure). Determine the value of that results in a box with the maximum volume. Following the steps to solve the problem. (1) Express the volume V as a function of x: V = (2) Determine the domain of the function V of x (use interval notation): (3) Find the derivative of the function V: V' = (4) Find the critical point(s) in the domain of V: (5) The value of V at the left endpoint is (6) The value of V at the right endpoint is (7) The maximum volume is V= (8) Answer the original question. The value of x that maximizes the volume is:
Transcribed Image Text:A box with no top is made from a rectangle with dimensions a = 15 inches by b= 11 inches by cutting a square of side x at each corner and turning up the sides (see the figure). Determine the value of that results in a box with the maximum volume. Following the steps to solve the problem. (1) Express the volume V as a function of x: V = (2) Determine the domain of the function V of x (use interval notation): (3) Find the derivative of the function V: V' = (4) Find the critical point(s) in the domain of V: (5) The value of V at the left endpoint is (6) The value of V at the right endpoint is (7) The maximum volume is V= (8) Answer the original question. The value of x that maximizes the volume is:
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