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Both first partial derivatives of the function f(x,y) are zero at the given points. Use the second-derivative test to determine the nature of f(x,y) at each of these points. If the second-derivative test is inconclusive, so state. f(x,y) = - 9x + 18xy - y° +81y; (- 3, - 3), (9,9) What is the nature of the function at (-3, - 3)? O A. f(x,y) has a relative minimum at (- 3, - 3). O B. f(x,y) has neither a relative maximum nor a relative minimum at (-3, - 3). O C. f(x,y) has a relative maximum at (- 3, - 3). O D. The second-derivative test is inconclusive at (- 3, - 3). What is the nature of the function at (9,9)? O A. f(x,y) has a relative minimum at (9,9). O B. f(x,y) has neither a relative maximum nor a relative minimum at (9,9). O C. f(x,y) has a relative maximum at (9,9). O D. The second-derivative test is inconclusive at (9,9).

Both first partial derivatives of the function f(x,y) are zero at the given points. Use the second-derivative test to determine the nature of f(x,y) at each of these points. If the second-derivative test is inconclusive, so state. f(x,y) = - 9x + 18xy - y° +81y; (- 3, - 3), (9,9) What is the nature of the function at (-3, - 3)? O A. f(x,y) has a relative minimum at (- 3, - 3). O B. f(x,y) has neither a relative maximum nor a relative minimum at (-3, - 3). O C. f(x,y) has a relative maximum at (- 3, - 3). O D. The second-derivative test is inconclusive at (- 3, - 3). What is the nature of the function at (9,9)? O A. f(x,y) has a relative minimum at (9,9). O B. f(x,y) has neither a relative maximum nor a relative minimum at (9,9). O C. f(x,y) has a relative maximum at (9,9). O D. The second-derivative test is inconclusive at (9,9).

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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Both first partial derivatives of the function f(x,y) are zero at the given points. Use the second-derivative test to determine the nature of f(x,y) at each of these points. If the second-derivative test is inconclusive, so state. f(x,y) = - 9x + 18xy - y° +81y; (- 3, – 3), (9,9) What is the nature of the function at (- 3, - 3)? A. f(x,y) has a relative minimum at (- 3, - 3). B. f(x,y) has neither a relative maximum nor a relative minimum at (- 3,– 3). C. f(x,y) has a relative maximum at (- 3, - 3). D. The second-derivative test is inconclusive at (- 3, - 3). What is the nature of the function at (9,9)? A. f(x,y) has a relative minimum at (9,9). B. f(x,y) has neither a relative maximum nor a relative minimum at (9,9). C. f(x,y) has a relative maximum at (9,9). D. The second-derivative test is inconclusive at (9,9). O O
Transcribed Image Text:Both first partial derivatives of the function f(x,y) are zero at the given points. Use the second-derivative test to determine the nature of f(x,y) at each of these points. If the second-derivative test is inconclusive, so state. f(x,y) = - 9x + 18xy - y° +81y; (- 3, – 3), (9,9) What is the nature of the function at (- 3, - 3)? A. f(x,y) has a relative minimum at (- 3, - 3). B. f(x,y) has neither a relative maximum nor a relative minimum at (- 3,– 3). C. f(x,y) has a relative maximum at (- 3, - 3). D. The second-derivative test is inconclusive at (- 3, - 3). What is the nature of the function at (9,9)? A. f(x,y) has a relative minimum at (9,9). B. f(x,y) has neither a relative maximum nor a relative minimum at (9,9). C. f(x,y) has a relative maximum at (9,9). D. The second-derivative test is inconclusive at (9,9). O O
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