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Let x cm be the length of a rectangular box. Then the dimensions of the box are shown as below. 9-x 2x 2x a) Show that the volume of the box can be written as V(x) = 4x²(9 – x). b) Copy and fill in the table: -3 0. 3 6. 10 V(x) c) Sketch the volume function. d) What is the domain of the function i) in general? ii) for this context? e) What is the range of the function i) in general? ii) for this context? e) Estimate the length that gives the maximum volume?

Let x cm be the length of a rectangular box. Then the dimensions of the box are shown as below. 9-x 2x 2x a) Show that the volume of the box can be written as V(x) = 4x²(9 – x). b) Copy and fill in the table: -3 0. 3 6. 10 V(x) c) Sketch the volume function. d) What is the domain of the function i) in general? ii) for this context? e) What is the range of the function i) in general? ii) for this context? e) Estimate the length that gives the maximum volume?

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter9: Surfaces And Solids
Section9.3: Cylinders And Cones
Problem 7E: The tin can shown at the right has the indicated dimensions. Estimate the number of square inches of...
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Let x cm be the length of a rectangular box. Then the dimensions of the box are shown as below. 9- x 2x 2x a) Show that the volume of the box can be written as V(x) = 4x²(9 – x). b) Copy and fill in the table: -3 3 6. 9. 10 V(x) c) Sketch the volume function. d) What is the domain of the function i) in general? ii) for this context? e) What is the range of the function i) in general? ii) for this context? e) Estimate the length that gives the maximum volume?
Transcribed Image Text:Let x cm be the length of a rectangular box. Then the dimensions of the box are shown as below. 9- x 2x 2x a) Show that the volume of the box can be written as V(x) = 4x²(9 – x). b) Copy and fill in the table: -3 3 6. 9. 10 V(x) c) Sketch the volume function. d) What is the domain of the function i) in general? ii) for this context? e) What is the range of the function i) in general? ii) for this context? e) Estimate the length that gives the maximum volume?
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