Open-box Problem. An open-box (top open) is made from a rectangular material of dimensions a = 14 inches by b= 10 inches by cutting a square of side at each corner and turning up the sides (see the figure). Determine the value of that results in a box the maximum volume. 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 : V = (2) Determine the domain of the function V of a (in interval form): (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. Type here to search
Open-box Problem. An open-box (top open) is made from a rectangular material of dimensions a = 14 inches by b= 10 inches by cutting a square of side at each corner and turning up the sides (see the figure). Determine the value of that results in a box the maximum volume. 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 : V = (2) Determine the domain of the function V of a (in interval form): (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. Type here to search
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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Transcribed Image Text:Open-box Problem. An open-box (top open) is made from a rectangular material of dimensions a = 14 inches by
b= 10 inches by cutting a square of side at each corner and turning up the sides (see the figure). Determine the
value of that results in a box the maximum volume.
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 : V =
(2) Determine the domain of the function V of a (in interval form):
(3) Expand the function V for easier differentiation: V =
(4) Find the derivative of the function VV' =
(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.
Type here to search
Transcribed Image Text:(7) The value of V at the right endpoint is
(8) The maximum volume is V =
(9) Answer the original question. The value of that maximizes the volume is:
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