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I just started Calculus 3 and I thought it would be useful to see images of functions to get used to the transition of visualizing in 3-dimensions. I was wondering how one would go about plotting a function like:

$$x^2 - y^2 + xy$$

And what would be the code to find its maxima and minima? I have never used Mathematica before so it would be of big help if you could show me the way to plot functions like this one. Thanks a lot.

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    $\begingroup$ Plot3D $\endgroup$ – Edmund Apr 18 '16 at 2:44
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Plot3D[x^2 - y^2 + x*y, {x, -10, 10}, {y, -10, 10}]

Which outputs a 3D graph over the specified domains. You have to specify a domain in order to determine minimum or maximum as global minimum/maximum are at positive and negative infinity respectively.

It is pretty clear from the equation and the plot that there is a saddle point at (0,0) however.

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