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. 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....

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# Homework Help: Sketch contours for f(x,y)=y^2+2x^2-x^4

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