Let f(x,y) be a function which has a critical point at (1,-2) with continuous partial derivatives. Which of the following properties is enough to conclude that (1,-2) is a saddle point? I. fxx (1,-2) < 0 and fyy (1,-2 ) < 0. II. fxy (1,-2) < 0. III. fxx (1,-2) fyy (1,-2) < fxy (1,-2) fyx (1,-2). IV. fxx (1,-2) fyy (1,-2)=fxy (1,-2) fyx (1,-2) a. I b. III c. II d. IV
Let f(x,y) be a function which has a critical point at (1,-2) with continuous partial derivatives. Which of the following properties is enough to conclude that (1,-2) is a saddle point? I. fxx (1,-2) < 0 and fyy (1,-2 ) < 0. II. fxy (1,-2) < 0. III. fxx (1,-2) fyy (1,-2) < fxy (1,-2) fyx (1,-2). IV. fxx (1,-2) fyy (1,-2)=fxy (1,-2) fyx (1,-2) a. I b. III c. II d. IV
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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Question
q4:
Let f(x,y) be a function which has a critical point at (1,-2) with continuous partial derivatives. Which of the following properties is enough to conclude that (1,-2) is a saddle point?
I. fxx (1,-2) < 0 and fyy (1,-2 ) < 0.
II. fxy (1,-2) < 0.
III. fxx (1,-2) fyy (1,-2) < fxy (1,-2) fyx (1,-2).
IV. fxx (1,-2) fyy (1,-2)=fxy (1,-2) fyx (1,-2)
a.
I
b.
III
c.
II
d.
IV
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