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You construct an open box with locking tabs from a square piece of material, 24 inches on a side, by cutting equal squares from the corners and folding along the dashed lines (see figure, where M 24). Determine the length at each corner that will maximize the volume of the resulting box. Round your answers to two decimal places, if necessary. the side x of the equal square in. Complete the following parts. (a) Give a function f in the variable x for the quantity to be optimized. (x) = (b) State the domain of this function. (Enter your answer using interval notation.) (c) To determine the optimal value of the function f, we need the critical numbers of Belect- o. (d) These critical numbers are as follows. (Round your answers to two decimal places, if necessary. If a critical number is an endpoint of the domain, do NOT include it in your answer. Enter your answers as a comma-separated list, If an answer does not exist, enter DNE.)

You construct an open box with locking tabs from a square piece of material, 24 inches on a side, by cutting equal squares from the corners and folding along the dashed lines (see figure, where M 24). Determine the length at each corner that will maximize the volume of the resulting box. Round your answers to two decimal places, if necessary. the side x of the equal square in. Complete the following parts. (a) Give a function f in the variable x for the quantity to be optimized. (x) = (b) State the domain of this function. (Enter your answer using interval notation.) (c) To determine the optimal value of the function f, we need the critical numbers of Belect- o. (d) These critical numbers are as follows. (Round your answers to two decimal places, if necessary. If a critical number is an endpoint of the domain, do NOT include it in your answer. Enter your answers as a comma-separated list, If an answer does not exist, enter DNE.)

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 94E
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You construct an open box with locking tabs from a square piece of material, 24 inches on a side, by cutting equal squares from the corners and folding along the dashed lines (see figure, where M 24). Determine the length of the sidex of the equal square at each corner that will maximize the volume of the resulting box. Round your answers to two decimal places, if necessary. in. Complete the following parts. (a) Give a function f in the variable x for the quantity to be optimized. (x) 3= (b) State the domain of this function. (Enter your answer using interval notation.) To determine the optimal value of the function f, we need the critical numbers of Belect o (c) (d) These critical numbers are as follows. (Round your answers to two decimal places, if necessary. If a critical number is an endpoint of the domain, do NOT include it in your answer. Enter your answers as a comma-separated list, If an answer does not exist, enter DNE.) M
Transcribed Image Text:You construct an open box with locking tabs from a square piece of material, 24 inches on a side, by cutting equal squares from the corners and folding along the dashed lines (see figure, where M 24). Determine the length of the sidex of the equal square at each corner that will maximize the volume of the resulting box. Round your answers to two decimal places, if necessary. in. Complete the following parts. (a) Give a function f in the variable x for the quantity to be optimized. (x) 3= (b) State the domain of this function. (Enter your answer using interval notation.) To determine the optimal value of the function f, we need the critical numbers of Belect o (c) (d) These critical numbers are as follows. (Round your answers to two decimal places, if necessary. If a critical number is an endpoint of the domain, do NOT include it in your answer. Enter your answers as a comma-separated list, If an answer does not exist, enter DNE.) M
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