Find the critical points of the functions f (x, y) = x² + 2y² - 4y + 2x, g(x, y) = x² - 14xy + y Use the Second Derivative Test to determine the local minimum, local maximum, and saddle points. (Give your answer as a comma-separated list of points in the form (*, *) where needed. Express numbers in exact form. Use symbolic notation and fractions where needed. Enter DNE if the answer does not exist.)
Find the critical points of the functions f (x, y) = x² + 2y² - 4y + 2x, g(x, y) = x² - 14xy + y Use the Second Derivative Test to determine the local minimum, local maximum, and saddle points. (Give your answer as a comma-separated list of points in the form (*, *) where needed. Express numbers in exact form. Use symbolic notation and fractions where needed. Enter DNE if the answer does not exist.)
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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Transcribed Image Text:Find the critical points of the functions
f (x, y) = x² + 2y² - 4y + 2x, g(x, y) = x² - 14xy + y
Use the Second Derivative Test to determine the local minimum, local maximum, and saddle points.
(Give your answer as a comma-separated list of points in the form (*, *) where needed. Express numbers in exact form. Use
symbolic notation and fractions where needed. Enter DNE if the answer does not exist.)
local minimum(s): -3
Incorrect
local maximum(s): DNE
1
saddle point(s): 196
Incorrect
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