Given is a function f(x, y), with f(a, b) = fy (a, b) = fyy (a, b) = 0, fay (a, b) = 0 and all second order partial derivatives are continuous at the critical point (a, b). What can be said about the critical point using the second derivative test? The critical point is a local minimum. O The critical point is a local maximum. O The critical point is a saddle point. Nothing, as the second derivative test is inconclusive.
Given is a function f(x, y), with f(a, b) = fy (a, b) = fyy (a, b) = 0, fay (a, b) = 0 and all second order partial derivatives are continuous at the critical point (a, b). What can be said about the critical point using the second derivative test? The critical point is a local minimum. O The critical point is a local maximum. O The critical point is a saddle point. Nothing, as the second derivative test is inconclusive.
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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![Given is a function f(x, y), with f(a, b) = f,(a, b) = fyy (a, b) = 0, fry (a, b) #0 and all second order
partial derivatives are continuous at the critical point (a, b). What can be said about the critical point using
the second derivative test?
O The critical point is a local minimum.
O The critical point is a local maximum.
O The critical point is a saddle point.
O Nothing, as the second derivative test is inconclusive.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2b33a8c0-f1ae-4a2f-8b6f-1af4247b3f3d%2Ffd8440b6-5646-4925-9032-fb37c6ac5364%2Fnu8p5o_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Given is a function f(x, y), with f(a, b) = f,(a, b) = fyy (a, b) = 0, fry (a, b) #0 and all second order
partial derivatives are continuous at the critical point (a, b). What can be said about the critical point using
the second derivative test?
O The critical point is a local minimum.
O The critical point is a local maximum.
O The critical point is a saddle point.
O Nothing, as the second derivative test is inconclusive.
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