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ΜΥΝΟTES ASK YOUR TEAC Find the local maximum and minimum values and saddle point(s) of the function. If yóu have three-dimensional graphing software, graph the function with a domaln and viewpoint that reveal al the important aspects of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) f(x, y) = x - 27xy + 27y3 local maximum value(s) local minimum value(s) (x, y, ) = saddle point(s)

ΜΥΝΟTES ASK YOUR TEAC Find the local maximum and minimum values and saddle point(s) of the function. If yóu have three-dimensional graphing software, graph the function with a domaln and viewpoint that reveal al the important aspects of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) f(x, y) = x - 27xy + 27y3 local maximum value(s) local minimum value(s) (x, y, ) = saddle point(s)

Advanced Engineering Mathematics
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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Find the local maximum and minimum values and saddle point(s) of the function. If you have three-dimensional graphing software, graph the function with a domaln and viewpoint that reveal all the important aspects of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) f(x, y) = x³ - 27xy + 27y3 local maximum value(s) ΜYΝΟTES ASK YOUR TEACP local minimum value(s) saddle point(s) (x, y, f) = Need Help? Read It Watch It Master It Submit Answer View Previous Question Question 3 of 8 View Next Question Home My Assignments O Request Extension Copyright © 1998 - 2021 Cengage Learning Inc. All Rights Reserved TERMS OF USE PRIVACY 19 F7 888 F6 80 F5 F4 1 F3 delete F2 & esc F1 $ 7 8. # 6. @ 4 3 P 1 U Y E re W J .. .-
Transcribed Image Text:Find the local maximum and minimum values and saddle point(s) of the function. If you have three-dimensional graphing software, graph the function with a domaln and viewpoint that reveal all the important aspects of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) f(x, y) = x³ - 27xy + 27y3 local maximum value(s) ΜYΝΟTES ASK YOUR TEACP local minimum value(s) saddle point(s) (x, y, f) = Need Help? Read It Watch It Master It Submit Answer View Previous Question Question 3 of 8 View Next Question Home My Assignments O Request Extension Copyright © 1998 - 2021 Cengage Learning Inc. All Rights Reserved TERMS OF USE PRIVACY 19 F7 888 F6 80 F5 F4 1 F3 delete F2 & esc F1 $ 7 8. # 6. @ 4 3 P 1 U Y E re W J .. .-
Expert Solution
Step 1

Compute fx, fy then equate them to 0 and solve for x and y to find the critical points.

 

Then, compute fxx , fyy and fxy .

 

Let (x,y) be a critical point.

D(x,y) is calculated using the formula : D(x,y)=fxx(x,y)fyy(x,y)-f2xy(x,y) .

If, D(x,y)>0, fxx(x,y)<0 then (x,y) is a local maximum.

If, D(x,y)>0, fxx(x,y)>0 then (x,y) is a local minimum.

If, D(x,y)<0, then (x,y) is a saddle point.

 

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