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(b) Write the volume V as a function of x. V = 0 < x < 15 (c) Use calculus to find the critical number of the function in part (b) and find the maximum value. V =

(b) Write the volume V as a function of x. V = 0 < x < 15 (c) Use calculus to find the critical number of the function in part (b) and find the maximum value. V =

Algebra & Trigonometry with Analytic Geometry
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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answer b and c correctly
HER An open box of maximum volume is to be made from a square piece of material, s = 30 centimeters on a side, by cutting equal squares from the corners ana turning up the sides (see figure). 21 (a) Analytically complete six rows of a table such as the one below. (The first two rows are shown.) Height, x Length and Width Volume, V 1 30 - 2(1) 1[30 - 2(1)]2 = 784 30 - 2(2) 2[30 - 2(2)]2 = 1352 2 3 30 - 2(3) 3[30 – 2(3)]? =| 4 30 – 2(4) |4[30 – 2(4)]2 = | 30 - 2(5) 5(30 – 2(5)]² = 6 30 - 2(6) 6[ 30 – 2(6)]2 = Use the table to guess the maximum volume. V = (b) Write the volume V as a function of x.
Transcribed Image Text:HER An open box of maximum volume is to be made from a square piece of material, s = 30 centimeters on a side, by cutting equal squares from the corners ana turning up the sides (see figure). 21 (a) Analytically complete six rows of a table such as the one below. (The first two rows are shown.) Height, x Length and Width Volume, V 1 30 - 2(1) 1[30 - 2(1)]2 = 784 30 - 2(2) 2[30 - 2(2)]2 = 1352 2 3 30 - 2(3) 3[30 – 2(3)]? =| 4 30 – 2(4) |4[30 – 2(4)]2 = | 30 - 2(5) 5(30 – 2(5)]² = 6 30 - 2(6) 6[ 30 – 2(6)]2 = Use the table to guess the maximum volume. V = (b) Write the volume V as a function of x.
5 30 – 2(5) 5[30 – 2(5)]² 6 30 – 2(6) 6[30 – 2(6)]² = Use the table to guess the maximum volume. V = (b) Write the volume V as a function of x. V = 0 < x < 15 (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 2000 2000아 1500 1500 1000 1000 500아 500
Transcribed Image Text:5 30 – 2(5) 5[30 – 2(5)]² 6 30 – 2(6) 6[30 – 2(6)]² = Use the table to guess the maximum volume. V = (b) Write the volume V as a function of x. V = 0 < x < 15 (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 2000 2000아 1500 1500 1000 1000 500아 500
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