O If fæz >0 and fyy <0 at a point (x, y) then (x, y) is a saddle point of f. If faa >0 and fyy> 0 at a point(r, y) then the point (x, y) is a local minimum of the function f. O If f(x, y) -L as (x, y) → (a, b) along every straight line through (a, b), then lim (2,v) (a,b) f(x, y) = L %3D

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Which of the following is true?
(There could be more than one correct answer)
O If fe >0 and fyy <0 at a point (x, y) then (x, y) is a saddle point of f.
O If fea > 0 and fy > 0 at a point(r, y) then the point (r, y) is a local minimum of the function f.
O If f(x, y) → L as (x, y) → (a, b) along every straight line through (a, b). then
lim
(2,y)(a,b)
f(x, y) = L
O For any unit vector u and any point (a, b)
Df(a, b) = -D f(a, b).
O The binormal vector of a curve r(t) is given by
B(t) = N(t) x T(t)
%3D
O The intersection of two non-parallel planes is always a straight line.
Transcribed Image Text:Which of the following is true? (There could be more than one correct answer) O If fe >0 and fyy <0 at a point (x, y) then (x, y) is a saddle point of f. O If fea > 0 and fy > 0 at a point(r, y) then the point (r, y) is a local minimum of the function f. O If f(x, y) → L as (x, y) → (a, b) along every straight line through (a, b). then lim (2,y)(a,b) f(x, y) = L O For any unit vector u and any point (a, b) Df(a, b) = -D f(a, b). O The binormal vector of a curve r(t) is given by B(t) = N(t) x T(t) %3D O The intersection of two non-parallel planes is always a straight line.
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