alyssalynn
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- Oct 20, 2010
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The behavior of a function can be complicated near a critical point where D=0. Suppose that f(x,y)= x^3 - 3xy^2.
a.) Show that there is one critical point at (0,0) and that D=0 at that point.
b.) Show that the contour for f(x,y)=0 consists of three lines intersecting at the origin where f alternates from positive to negative. Sketch a contour diagram for f near 0.
I've already done part a, but I don't have any idea how to start part b. We haven't done anything like this in class, it isn't in the book, and I can't find a similar problem online. Please help!
a.) Show that there is one critical point at (0,0) and that D=0 at that point.
b.) Show that the contour for f(x,y)=0 consists of three lines intersecting at the origin where f alternates from positive to negative. Sketch a contour diagram for f near 0.
I've already done part a, but I don't have any idea how to start part b. We haven't done anything like this in class, it isn't in the book, and I can't find a similar problem online. Please help!