- #1
mrchartreuse
- 3
- 0
The problem is:
. Let f : R^2 → R be given by f(x,y)=y^2 +2x^2 −x^4.
Sketch the contour diagram of f by drawing the contours f = −2, −1, 0, 1 , 1, 2.
I have started with the f = -1 line and managed to get it into a form resembling a hyperbola:
1 = (x^2-1)^2/2 - y^2/2
Is this the right sort of approach? And if so how would i sketch this with the x^2 where the x usually is?
I was thinking of trying to sketch it with all the values along the x-axis square rooted or something so it would look like a sort of squashed hyperbola but since a square root has two possible answers I don't think this is correct... Then there are all the other scary f values...
. Let f : R^2 → R be given by f(x,y)=y^2 +2x^2 −x^4.
Sketch the contour diagram of f by drawing the contours f = −2, −1, 0, 1 , 1, 2.
I have started with the f = -1 line and managed to get it into a form resembling a hyperbola:
1 = (x^2-1)^2/2 - y^2/2
Is this the right sort of approach? And if so how would i sketch this with the x^2 where the x usually is?
I was thinking of trying to sketch it with all the values along the x-axis square rooted or something so it would look like a sort of squashed hyperbola but since a square root has two possible answers I don't think this is correct... Then there are all the other scary f values...