level curves for -(x^2 + y^2)?
how would you draw the level curves for f(x,y)= -(x^2+y^2). the way i see it, since the function in the parentheses is a circle, the level curves will be below the horizon in an x,y plain. so, like a semi-circle....???
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The level curve for a function f(x,y) is obtained by simply letting that function = a constant.
f(x,y) = -(x^2+y^2) = k --> x^2+ y^2 = -k
This is a family of circles with the center at the origin.