The problem is:(adsbygoogle = window.adsbygoogle || []).push({});

. 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....

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

**Physics Forums | Science Articles, Homework Help, Discussion**