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Open-box Problem. An open-box (top open) is made from a rectangular material of dimensions a = 8 inches by b = 7 inches by cutting a square of side x at each corner and turning up the sides (see the figure). Determine the value of a that results in a box the maximum volume.

Open-box Problem. An open-box (top open) is made from a rectangular material of dimensions a = 8 inches by b = 7 inches by cutting a square of side x at each corner and turning up the sides (see the figure). Determine the value of a that results in a box the maximum volume.

PREALGEBRA
PREALGEBRA
15th Edition
ISBN:9781938168994
Author:OpenStax
Publisher:OpenStax
Chapter9: Math Models And Geometry
Section9.6: Solve Geometry Applications: Volume And Surface Area
Problem 304E: Ice cream cones A regular ice cream cone is 4 inches tall and has a diameter of 2.5 inches, A waffle...
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(3) Expand the function V for easier differentiation: V = (4) Find the derivative of the function V: V' (5) Find the critical point(s) in the domain of V: (6) The value of V at the left endpoint is (7) The value of V at the right endpoint is (8) The maximum volume is V
Transcribed Image Text:(3) Expand the function V for easier differentiation: V = (4) Find the derivative of the function V: V' (5) Find the critical point(s) in the domain of V: (6) The value of V at the left endpoint is (7) The value of V at the right endpoint is (8) The maximum volume is V
Open-box Problem. An open-box (top open) is made from a rectangular material of dimensions a = 8 inches by b corner and turning up the sides (see the figure). Determine the value of x that results in a box the maximum volume. 7 inches by cutting a square of side x at each +8+ a 7- 6 4 3- Following the steps to solve the problem. Check Show Answer only after you have tried hard. (1) Express the volume V as a function of x: V (2) Determine the domain of the function V of x (in interval form):
Transcribed Image Text:Open-box Problem. An open-box (top open) is made from a rectangular material of dimensions a = 8 inches by b corner and turning up the sides (see the figure). Determine the value of x that results in a box the maximum volume. 7 inches by cutting a square of side x at each +8+ a 7- 6 4 3- Following the steps to solve the problem. Check Show Answer only after you have tried hard. (1) Express the volume V as a function of x: V (2) Determine the domain of the function V of x (in interval form):
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