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Problem 1. Find the local maximum and minimum values (and their locations) and any saddle point(s) of the following functions: (a) f(x, y) = x² + xy + y² + y Local min of -1/3 at the location (x, y) = (1/3, -2/3) (b) g(x, y) = xy - 2x - 2y — x² - y² Local max of 4 at the location (x, y) = (−2, −2) (c) f(x, y) = y³ + 3x²y 6x² - 6y² + 2 Local max of 2 at the location (x, y) = (0,0) Local min of -30 at the location (x, y) = (0.4) Saddle point of (-2,2,-14) Saddle point of (2,2, -14)

Problem 1. Find the local maximum and minimum values (and their locations) and any saddle point(s) of the following functions: (a) f(x, y) = x² + xy + y² + y Local min of -1/3 at the location (x, y) = (1/3, -2/3) (b) g(x, y) = xy - 2x - 2y — x² - y² Local max of 4 at the location (x, y) = (−2, −2) (c) f(x, y) = y³ + 3x²y 6x² - 6y² + 2 Local max of 2 at the location (x, y) = (0,0) Local min of -30 at the location (x, y) = (0.4) Saddle point of (-2,2,-14) Saddle point of (2,2, -14)

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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Problem 1. Find the local maximum and minimum values (and their locations) and any saddle point (s) of the following functions: (a) f(x, y) = x² + xy + y² + y Local min of -1/3 at the location (x, y) = (1/3, −2/3) (b) g(x, y) = xy 1 - 2x - 2y — x² − y ² Local max of 4 at the location (x, y) = (−2, −2) (c) f(x, y) = y³ + 3x²y − 6x² − 6y² +2 Local max of 2 at the location (x, y) = (0,0) Local min of -30 at the location (x, y) = (0.4) Saddle point of (-2,2, -14) Saddle point of (2,2, -14)
Transcribed Image Text:Problem 1. Find the local maximum and minimum values (and their locations) and any saddle point (s) of the following functions: (a) f(x, y) = x² + xy + y² + y Local min of -1/3 at the location (x, y) = (1/3, −2/3) (b) g(x, y) = xy 1 - 2x - 2y — x² − y ² Local max of 4 at the location (x, y) = (−2, −2) (c) f(x, y) = y³ + 3x²y − 6x² − 6y² +2 Local max of 2 at the location (x, y) = (0,0) Local min of -30 at the location (x, y) = (0.4) Saddle point of (-2,2, -14) Saddle point of (2,2, -14)
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