Find the critical points of the functions f (x, y) = x² + 2y² − 4y + 2x, g (x, y) = x² — 12xy + 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).
Find the critical points of the functions f (x, y) = x² + 2y² − 4y + 2x, g (x, y) = x² — 12xy + 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).
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 − 12xy + 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):
local maximum(s): DNE
saddle point(s):
Match f (x, y) and g (x, y) with their graphs.
g (x, y)
(A)
(B)
f (x, y)
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