Homework Help is Here – Start Your Trial Now!
Math
Calculus
3 4.6 Homework-Optimization WA 4.6 Homework-Optimization -X W 4.5 Homework-Indet Forms - MX -> -> O 8 https://www.webassign.net/web/Student/Assignment-Responses/submit?pos=1&dep%=D28532310&tags=autosave# E O ONE DRIVE EMAIL Getting Started CANVAS A = 2nr + 2nrh To eliminateh we use the fact that the volume is qiven as 3600 cm', Thus nr'h = 3600 which gives Area 2(er') Area (2 rh 3600 Substitution of this into the expression for A gives 3600 A = 2nr' + 2nr y 3600- 7200 = 2nr + Therefore the function we want to minimize is 20 A (r) = 2ar2 + 7200 ,r>0 %3D Video Example ) r To find the critical numbers, we differentiate: 7200 A'(r) = 4nr - 7:57 PM 70°F Clear 4/4/2022 2 Type here to search Ip

3 4.6 Homework-Optimization WA 4.6 Homework-Optimization -X W 4.5 Homework-Indet Forms - MX -> -> O 8 https://www.webassign.net/web/Student/Assignment-Responses/submit?pos=1&dep%=D28532310&tags=autosave# E O ONE DRIVE EMAIL Getting Started CANVAS A = 2nr + 2nrh To eliminateh we use the fact that the volume is qiven as 3600 cm', Thus nr'h = 3600 which gives Area 2(er') Area (2 rh 3600 Substitution of this into the expression for A gives 3600 A = 2nr' + 2nr y 3600- 7200 = 2nr + Therefore the function we want to minimize is 20 A (r) = 2ar2 + 7200 ,r>0 %3D Video Example ) r To find the critical numbers, we differentiate: 7200 A'(r) = 4nr - 7:57 PM 70°F Clear 4/4/2022 2 Type here to search Ip

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
See similar textbooks
icon
Related questions
Question
Please help, this is one full question.
TRI N Sudku les THE 7% DEATH. EVELYN HARDCAS TOR 8 4.6 Homework-Optimization WA 4.6 Homework-Optimization - X W 4.5 Homework-Indet Forms - M X + 8 https://www.webassign.net/web/Student/Assignment-Responses/submit?pos=1&dep=28532310&tags=autosave# E WILEY O ONE DRIVE O EMAIL Getting Started CANVAS O M A = 2nr + 2nrh To eliminateh we use the fact that the volume is given as 3600 cm. Thus nr'h = 3600 which gives h = Area 2(mr') Area (2rh 3600 . Substitution of this into the expression for A gives 3600 A = 2nr' + 2nr( y 3600- 7200 = 2nr? + Therefore the function we want to minimize is 20 7200 A (r) = 2ar² + Video Example r>0 To find the critical numbers, we differentiate: 7200 A'(r) = 4nr - 7:57 PM 中 2 70°F Clear 4/4/2022 P Type here to search AT
Transcribed Image Text:TRI N Sudku les THE 7% DEATH. EVELYN HARDCAS TOR 8 4.6 Homework-Optimization WA 4.6 Homework-Optimization - X W 4.5 Homework-Indet Forms - M X + 8 https://www.webassign.net/web/Student/Assignment-Responses/submit?pos=1&dep=28532310&tags=autosave# E WILEY O ONE DRIVE O EMAIL Getting Started CANVAS O M A = 2nr + 2nrh To eliminateh we use the fact that the volume is given as 3600 cm. Thus nr'h = 3600 which gives h = Area 2(mr') Area (2rh 3600 . Substitution of this into the expression for A gives 3600 A = 2nr' + 2nr( y 3600- 7200 = 2nr? + Therefore the function we want to minimize is 20 7200 A (r) = 2ar² + Video Example r>0 To find the critical numbers, we differentiate: 7200 A'(r) = 4nr - 7:57 PM 中 2 70°F Clear 4/4/2022 P Type here to search AT
HIONE SUDU l THE 7% DEATH. EVELYN HARDCAL TOR 8 4.6 Homework-Optimization WA 4.6 Homework-Optimization X W 4.5 Homework-Indet Forms - M X + -> 8 https://www.webassign.net/web/Student/Assignment-Responses/submit?pos=1&dep=285323108&tags=autosave#q E * WILE O ONE DRIVE O EMAIL Getting Started 8 CANVAS 4( Your answer cannot be understood or graded. More Information) CUE Then A'(r) = 0 when = 1800, so the only critical number is r = Since the domain of A is (0, 0), we can't use the endpoint arguments to determine if the critical point is a maximum or a minimum. But we can observe that A'(r) < O for r < and A'(r) > 0 for r> , so A is decreasing for all r to the left of the critical number and increasing for all r to the right. Thus r = must give give the absolute minimum. [Alternatively, we could argue that A(r) – o as r+ 0* and A(r) → o as r+ n, so there must be a minimum value of A(r), which must occur at the critical number. See the graph.] The value of h corresponding to r = 'V1800/n is 3600 3600 h = = 2r %3D 7:57 PM 70°F Clear 4/4/2022 P Type here to search Iyp ICT SAT
Transcribed Image Text:HIONE SUDU l THE 7% DEATH. EVELYN HARDCAL TOR 8 4.6 Homework-Optimization WA 4.6 Homework-Optimization X W 4.5 Homework-Indet Forms - M X + -> 8 https://www.webassign.net/web/Student/Assignment-Responses/submit?pos=1&dep=285323108&tags=autosave#q E * WILE O ONE DRIVE O EMAIL Getting Started 8 CANVAS 4( Your answer cannot be understood or graded. More Information) CUE Then A'(r) = 0 when = 1800, so the only critical number is r = Since the domain of A is (0, 0), we can't use the endpoint arguments to determine if the critical point is a maximum or a minimum. But we can observe that A'(r) < O for r < and A'(r) > 0 for r> , so A is decreasing for all r to the left of the critical number and increasing for all r to the right. Thus r = must give give the absolute minimum. [Alternatively, we could argue that A(r) – o as r+ 0* and A(r) → o as r+ n, so there must be a minimum value of A(r), which must occur at the critical number. See the graph.] The value of h corresponding to r = 'V1800/n is 3600 3600 h = = 2r %3D 7:57 PM 70°F Clear 4/4/2022 P Type here to search Iyp ICT SAT
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Precalculus
Precalculus
Calculus
ISBN:
9780135189405
Author:
Michael Sullivan
Publisher:
PEARSON
Calculus: Early Transcendental Functions
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS