TITLE: Level Curves
# !b2 Problem:
Sketch the level curves of the function,
!c0 f(x,y) = x^3 -y

!b3 Solution:

> with(plots):
> contourplot(x^3-y,x=-2..2,y=-2..2,contours=[0,1,2]);
# This command produces the level curves at levels 0,1 and 2.
!im contours.gif
# Notice that these are the cubics 
!c0 y = x^3 - c
that intersect the x-axis at x=c^(1/3)

>