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Mathematics 1
Mathematics 1 Deneme Sınavı
Mathematics 1 Deneme Sınavı Sorusu #1233645
Mathematics 1 Deneme Sınavı Sorusu #1233645
How many of the following points are stationary points for the function f(x,y)=x4+x2y2-2x2+2y2?
I.(0,0)
II.(1,0)
III.(1,1)
IV. (-1,0)
V.(0,?2)
|
5 |
|
4 |
|
3 |
|
2 |
|
1 |
Yanıt Açıklaması:
f(x,y)=x4+x2y2-2x2+2y2?
We have to find the points simultaneously satisfy fx=0 and fy=0
fx=4x3+2xy2-4x=0, so x(4x2+2y2-4)=0
fy=2x2y+4y=0, so y(2x2+4)=0
Points given in III and V doesnt satisfy these conditions simultaneously. So the remaining 3 points are stationary points.
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