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(d) Use a graphing utility to graph the function in part (b) and verify the maximum volume from the graph. V V 200 150 100 50 V 400 300 200 100 2 2 4 4 6 6 8 8 X 50 40 30 20 10 V 400 300 200 100 1 2 2 4 3 6 4 8 X X

(d) Use a graphing utility to graph the function in part (b) and verify the maximum volume from the graph. V V 200 150 100 50 V 400 300 200 100 2 2 4 4 6 6 8 8 X 50 40 30 20 10 V 400 300 200 100 1 2 2 4 3 6 4 8 X X

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Calculus 1 Optimization

(d) Use a graphing utility to graph the function in part (b) and verify the maximum volume from the graph. V 200 150 100 50 400 300 200 100 2 2 4 6 6 8 8 X X 50 40 30 20 10 400 300 200 100 1 2 2 4 3 6 4 8 X X
Transcribed Image Text:(d) Use a graphing utility to graph the function in part (b) and verify the maximum volume from the graph. V 200 150 100 50 400 300 200 100 2 2 4 6 6 8 8 X X 50 40 30 20 10 400 300 200 100 1 2 2 4 3 6 4 8 X X
An open box of maximum volume is to be made from a square piece of material, s = 18 inches on a side, by cutting equal squares from the corners and turning up the sides (see figure). s - 2x X (a) Analytically complete six rows of a table such as the one below. (The first two rows are shown.) Length and Width 18 - 2(1) 18 - 2(2) 182(3) 3[18 – 2(3)]² = 182(4) 4[18 – 2(4)]² = 182(5) 5[18 — 2(5)]² = 182(6) 6[18 – 2(6)]² = V = Height, x 1 2 3 4 5 s-2x- 6 Use the table to guess the maximum volume. V = Volume, V 1[182(1)]²= 256 2[182(2)]² = 392 (b) Write the volume V as a function of x. 0 < x < 9 (c) Use calculus to find the critical number of the function in part (b) and find the maximum value. V =
Transcribed Image Text:An open box of maximum volume is to be made from a square piece of material, s = 18 inches on a side, by cutting equal squares from the corners and turning up the sides (see figure). s - 2x X (a) Analytically complete six rows of a table such as the one below. (The first two rows are shown.) Length and Width 18 - 2(1) 18 - 2(2) 182(3) 3[18 – 2(3)]² = 182(4) 4[18 – 2(4)]² = 182(5) 5[18 — 2(5)]² = 182(6) 6[18 – 2(6)]² = V = Height, x 1 2 3 4 5 s-2x- 6 Use the table to guess the maximum volume. V = Volume, V 1[182(1)]²= 256 2[182(2)]² = 392 (b) Write the volume V as a function of x. 0 < x < 9 (c) Use calculus to find the critical number of the function in part (b) and find the maximum value. V =
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