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8. DETAILS A rectangular storage container with an open top is to have a capacity of 101 in.³. The length of this base is 4 times the width. What should the dimensions of the container be to minimize the construction cost? Let x be the width (in in.) of the base of the container, and h be the height (in in.) of the container. x = in. (Round your answer to two decimal places, if necessary.) Complete the following parts. Give a function f in the variable x for the quantity to be optimized. f(x) = (a) (b) State the domain of this function. (Enter your answer using interval notation.) (c) Give the formula for h in terms of x. h= (d) To determine the optimal value of the function f, we need the critical numbers of -Select- (e) To find these critical numbers, we need to find-Select--- MY NOTES Submit Answer ASK (f) These critical numbers are as follows. (Round your answer(s) 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-separ an answer does not exist, enter DNE.)

8. DETAILS A rectangular storage container with an open top is to have a capacity of 101 in.³. The length of this base is 4 times the width. What should the dimensions of the container be to minimize the construction cost? Let x be the width (in in.) of the base of the container, and h be the height (in in.) of the container. x = in. (Round your answer to two decimal places, if necessary.) Complete the following parts. Give a function f in the variable x for the quantity to be optimized. f(x) = (a) (b) State the domain of this function. (Enter your answer using interval notation.) (c) Give the formula for h in terms of x. h= (d) To determine the optimal value of the function f, we need the critical numbers of -Select- (e) To find these critical numbers, we need to find-Select--- MY NOTES Submit Answer ASK (f) These critical numbers are as follows. (Round your answer(s) 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-separ an answer does not exist, enter DNE.)

Mathematics For Machine Technology
Mathematics For Machine Technology
8th Edition
ISBN:9781337798310
Author:Peterson, John.
Publisher:Peterson, John.
Chapter59: Areas Of Rectangles, Parallelograms, And Trapezoids
Section: Chapter Questions
Problem 79A
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8. DETAILS webassign.net/web/Student/Assignment-Responses/submit?dep=29438643&tags=autosave#question5346563_2 A rectangular storage container with an open top is to have a capacity of 101 in.3. The length of this base is 4 times the width. What should the dimensions of the container be to minimize the construction cost? Let x be the width (in in.) of the base of the container, and h be the height (in in.) of the container. x = in. (Round your answer to two decimal places, if necessary.) Complete the following parts. (a) Give a function f in the variable x for the quantity to be optimized. 9. (b) f(x) = State the domain of this function. (Enter your answer using interval notation.) (c) Give the formula for h in terms of x. h= x = Submit Answer (d) To determine the optimal value of the function f, we need the critical numbers of ---Select--- ✓ (e) To find these critical numbers, we need to find -Select---- (f) These critical numbers are as follows. (Round your answer(s) 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-separa an answer does not exist, enter DNE.) DETAILS Exam Confirmation Type here to search O Bi 2 O 67 F8 F9 F10 F11 RR. MY NOTES F12 PrtScr MY NOTES Q 69°F Sunny ASK ASK YOUR TE 31 11/
Transcribed Image Text:8. DETAILS webassign.net/web/Student/Assignment-Responses/submit?dep=29438643&tags=autosave#question5346563_2 A rectangular storage container with an open top is to have a capacity of 101 in.3. The length of this base is 4 times the width. What should the dimensions of the container be to minimize the construction cost? Let x be the width (in in.) of the base of the container, and h be the height (in in.) of the container. x = in. (Round your answer to two decimal places, if necessary.) Complete the following parts. (a) Give a function f in the variable x for the quantity to be optimized. 9. (b) f(x) = State the domain of this function. (Enter your answer using interval notation.) (c) Give the formula for h in terms of x. h= x = Submit Answer (d) To determine the optimal value of the function f, we need the critical numbers of ---Select--- ✓ (e) To find these critical numbers, we need to find -Select---- (f) These critical numbers are as follows. (Round your answer(s) 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-separa an answer does not exist, enter DNE.) DETAILS Exam Confirmation Type here to search O Bi 2 O 67 F8 F9 F10 F11 RR. MY NOTES F12 PrtScr MY NOTES Q 69°F Sunny ASK ASK YOUR TE 31 11/
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