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Given the function f(x, y) = x² − y² + 9xy, list out the critical point(s) and define whether the critical point(s) is/ are local maximum, local minimum, or a saddle point. (x, y) = (0, 0) & (x, y) = (3, -3) (0, 0), f11*f22-(f12)^2 = -81 <0 (saddle point) (3, -3), 11*f22-(f12)^2 = 243> 0 (local min.)

Given the function f(x, y) = x² − y² + 9xy, list out the critical point(s) and define whether the critical point(s) is/ are local maximum, local minimum, or a saddle point. (x, y) = (0, 0) & (x, y) = (3, -3) (0, 0), f11*f22-(f12)^2 = -81 <0 (saddle point) (3, -3), 11*f22-(f12)^2 = 243> 0 (local min.)

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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1. Given the function f(x, y) = x² - y² + 9xy, list out the critical point(s) and define whether the critical point(s) is/ are local maximum, local minimum, or a saddle point. (x, y) = (0, 0) & (x, y) = (3, -3) (0, 0), f11*f22-(f12)^2 = -81 <0 (saddle point) (3,-3), 11*f22-(f12)^2 = 243 > 0 (local min.)
Transcribed Image Text:1. Given the function f(x, y) = x² - y² + 9xy, list out the critical point(s) and define whether the critical point(s) is/ are local maximum, local minimum, or a saddle point. (x, y) = (0, 0) & (x, y) = (3, -3) (0, 0), f11*f22-(f12)^2 = -81 <0 (saddle point) (3,-3), 11*f22-(f12)^2 = 243 > 0 (local min.)
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