f(x, y) = (6x-x²) (6y - y²). Find and classify all critical points of the function. If there are more blanks than critical points, leave the remaining entries blank. f = fy = fax = fry fyy There are several critical points to be listed. List them lexicograhically, that is in ascending order by x-coordinates, and for equal x-coordinates in ascending order by y-coordinates (e.g., (1, 1), (2, -1), (2, 3) is a correct order) The critical point with the smallest x-coordinate is ) Classification: (local minimum, local maximum, saddle point, cannot ( be determined) The critical point with the next smallest x-coordinate is ( ) Classification: be determined) The critical point with the next smallest x-coordinate is ( ) Classification: be determined) The critical point with the next smallest x-coordinate is ) Classification: be determined) The critical point with the next smallest x-coordinate is ( ) Classification: be determined) (local minimum, local maximum, saddle point, cannot (local minimum, local maximum, saddle point, cannot (local minimum, local maximum, saddle point, cannot (local minimum, local maximum, saddle point, cannot

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 94E
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Question
f(x, y) = (6x-x²) (6y - y²).
Find and classify all critical points of the function. If there are more blanks than critical points, leave the remaining entries blank. f₂ =
fy =
fax =
fry
=
fyy
There are several critical points to be listed. List them lexicograhically, that is in ascending order by x-coordinates, and for equal x-coordinates in ascending
order by y-coordinates (e.g., (1,1), (2, -1), (2, 3) is a correct order) The critical point with the smallest x-coordinate is
) Classification:
(local minimum, local maximum, saddle point, cannot
(
be determined)
The critical point with the next smallest x-coordinate is
(
) Classification:
be determined)
The critical point with the next smallest x-coordinate is
(
) Classification:
be determined)
The critical point with the next smallest x-coordinate is
) Classification:
be determined)
The critical point with the next smallest x-coordinate is
(
) Classification:
be determined)
(local minimum, local maximum, saddle point, cannot
(local minimum, local maximum, saddle point, cannot
(local minimum, local maximum, saddle point, cannot
(local minimum, local maximum, saddle point, cannot
Transcribed Image Text:f(x, y) = (6x-x²) (6y - y²). Find and classify all critical points of the function. If there are more blanks than critical points, leave the remaining entries blank. f₂ = fy = fax = fry = fyy There are several critical points to be listed. List them lexicograhically, that is in ascending order by x-coordinates, and for equal x-coordinates in ascending order by y-coordinates (e.g., (1,1), (2, -1), (2, 3) is a correct order) The critical point with the smallest x-coordinate is ) Classification: (local minimum, local maximum, saddle point, cannot ( be determined) The critical point with the next smallest x-coordinate is ( ) Classification: be determined) The critical point with the next smallest x-coordinate is ( ) Classification: be determined) The critical point with the next smallest x-coordinate is ) Classification: be determined) The critical point with the next smallest x-coordinate is ( ) Classification: be determined) (local minimum, local maximum, saddle point, cannot (local minimum, local maximum, saddle point, cannot (local minimum, local maximum, saddle point, cannot (local minimum, local maximum, saddle point, cannot
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