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Question

# use a computer to provide a portrait of the given function g(x, y). To do this, (a) use the computer to help you understand some of the level curves of the function, and (b) use the computer to graph (a portion of) the surface z = g(x, y). In addition, mark on your surface some of the contour curves corresponding to the level curves you obtained in part (a).$g(x, y) = x^2 − xy$

Solution

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Step 1
1 of 3

Like in previous examples we sketch the 3d shape in Geogebra first and we set the heights of level curves on $1$ and $2$ for the convenience. An equation of a level curve in $xy$ plane is given by:

$x^2-xy=1$

For the other curve we set the right side of equation on $2$ instead of $1$. Pictures are below.

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