An open box of maximum volume is to be made from a square piece of material, s = 24 centimeters on a side, by cutting equal squares from the corners and turning up the sides (see figure). (a) Analytically complete six rows of a table such as the one below. (The first two rows are shown.) Length and Width 24 - 2(1) 24 - 2(2) 24-2(3) 3[24 - 2(3)]² = [ 242(4) 4[24-2(4)]²=| 24-2(5) 5[24-2(5)]² = [ 242(6) 6[242(6)]²= Height, x 1 V = 2 3 4 5 s-2x 6 Use the table to guess the maximum volume. V = (b) Write the volume V as a function of x. Volume, V 1[242(1)]² 484 2[24 - 2(2)]² = 800 0 < x < 12 (c) Use calculus to find the critical number of the function in part (b) and find the maximum value. V= =
An open box of maximum volume is to be made from a square piece of material, s = 24 centimeters on a side, by cutting equal squares from the corners and turning up the sides (see figure). (a) Analytically complete six rows of a table such as the one below. (The first two rows are shown.) Length and Width 24 - 2(1) 24 - 2(2) 24-2(3) 3[24 - 2(3)]² = [ 242(4) 4[24-2(4)]²=| 24-2(5) 5[24-2(5)]² = [ 242(6) 6[242(6)]²= Height, x 1 V = 2 3 4 5 s-2x 6 Use the table to guess the maximum volume. V = (b) Write the volume V as a function of x. Volume, V 1[242(1)]² 484 2[24 - 2(2)]² = 800 0 < x < 12 (c) Use calculus to find the critical number of the function in part (b) and find the maximum value. V= =
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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