Maxima for maxima (and minima) of functions z=f(x,y)

Together with the 3D graphing capabilities of Maxima, we can bring  symbolic differentiation and the numerical solver to bear when we seek local extrema of a surface.

Here is a link to the html export of a wxMaxima session where I work on two examples from my multivariable calculus class.  And here is the wxMaxima session.