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10. Let f(x, y)= x – 24x + y – 10y. (3,2) is A) A relative maximum B) A relative minimum C) A saddle point D) Cannot be determined E) Both a relative maximum and a saddle point

10. Let f(x, y)= x – 24x + y – 10y. (3,2) is A) A relative maximum B) A relative minimum C) A saddle point D) Cannot be determined E) Both a relative maximum and a saddle point

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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**Problem 10:** Consider the function \( f(x, y) = x^3 - 24x + y^3 - 10y \). Determine the nature of the point \( (3, 2) \) as follows: A) A relative maximum B) A relative minimum C) A saddle point D) Cannot be determined E) Both a relative maximum and a saddle point The question involves assessing the critical point \( (3, 2) \) of a multivariable function to determine whether it is a point of local extremum or a saddle point.
Transcribed Image Text:**Problem 10:** Consider the function \( f(x, y) = x^3 - 24x + y^3 - 10y \). Determine the nature of the point \( (3, 2) \) as follows: A) A relative maximum B) A relative minimum C) A saddle point D) Cannot be determined E) Both a relative maximum and a saddle point The question involves assessing the critical point \( (3, 2) \) of a multivariable function to determine whether it is a point of local extremum or a saddle point.
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