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f(x, y) = (8x-x²) (10y - 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= fzz = 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

f(x, y) = (8x-x²) (10y - 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= fzz = 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

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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f(x, y) = (8x-x²) (10y - 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 = fzz = 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) = (8x-x²) (10y - 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 = fzz = 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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