An open box of maximum volume is to be made from a square piece of material, s = 12 inches on a side, by cutting equal squares from the coners and turning up the sides (see figure). S-2r X (a) Analytically complete six rows of a table such as the one below. (The first two rows are shown.) Height, xLength and Width Volume, V 12 2(1) 1 1[12 2(1)12 2[12 2(2)12 = 100 12 2(2) 2. = 128 3[12 2(3)12 12 2(3) 3 12 2(4) 4[12 2(4)]2 4 12 2(5) 5[12 2(5)]2 12 2(6) 6[12 2(6)]2 Use the table to quess the maximum volume. =A (b) Write the volume Vas a function of x. 0 x<6 (c) Use calculus to find the critical number of the function in part (b) and find the maximum value. V = (d) Use a graphing utility to graph the function in part (b) and verify the maximum volume from the graph. V V 120 15 100 80 10 60 40 20 X 2 4 5 6 X 0.5 1.0 1.5 2.0 2.5 3.0 V V 60 120 50 100 40 80 30 60 20 40 10 20 X 6 1 X 2 3 4 5 3 5 2 S 2r
An open box of maximum volume is to be made from a square piece of material, s = 12 inches on a side, by cutting equal squares from the coners and turning up the sides (see figure). S-2r X (a) Analytically complete six rows of a table such as the one below. (The first two rows are shown.) Height, xLength and Width Volume, V 12 2(1) 1 1[12 2(1)12 2[12 2(2)12 = 100 12 2(2) 2. = 128 3[12 2(3)12 12 2(3) 3 12 2(4) 4[12 2(4)]2 4 12 2(5) 5[12 2(5)]2 12 2(6) 6[12 2(6)]2 Use the table to quess the maximum volume. =A (b) Write the volume Vas a function of x. 0 x<6 (c) Use calculus to find the critical number of the function in part (b) and find the maximum value. V = (d) Use a graphing utility to graph the function in part (b) and verify the maximum volume from the graph. V V 120 15 100 80 10 60 40 20 X 2 4 5 6 X 0.5 1.0 1.5 2.0 2.5 3.0 V V 60 120 50 100 40 80 30 60 20 40 10 20 X 6 1 X 2 3 4 5 3 5 2 S 2r
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.4: Complex And Rational Zeros Of Polynomials
Problem 39E
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