You plan to make a box with a square base and lid, with the largest possible volume, and with surface area 140in^2 a) If the square base of the box is x inches wide, determine a formula for the function V (x) representing the volume of the box (in cubic inches). Your function should contain the variable x and cannot contain any other variables. b) Determine a domain for V(x) which makes sense in the context of the scenario. Briefly explain why you chose the domain you provided c) Determine the largest possible volume of such a box. You must use calculus to verify that the volume you find is the largest possible volume
You plan to make a box with a square base and lid, with the largest possible volume, and with surface area 140in^2 a) If the square base of the box is x inches wide, determine a formula for the function V (x) representing the volume of the box (in cubic inches). Your function should contain the variable x and cannot contain any other variables. b) Determine a domain for V(x) which makes sense in the context of the scenario. Briefly explain why you chose the domain you provided c) Determine the largest possible volume of such a box. You must use calculus to verify that the volume you find is the largest possible volume
Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter9: Polynomial And Rational Functions
Section9.4: Graphing Polynomial Functions
Problem 43PS
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You plan to make a box with a square base and lid, with the largest possible volume, and with surface area 140in^2
a) If the square base of the box is x inches wide, determine a formula for the function V (x) representing the volume of the box (in cubic inches). Your function should contain the variable x and cannot contain any other variables.
b) Determine a domain for V(x) which makes sense in the context of the scenario. Briefly explain why you chose the domain you provided
c) Determine the largest possible volume of such a box. You must use calculus to verify that the volume you find is the largest possible volume.
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