Solving one of these by hand: • Absolute Max/Min of Mu...
In this video we use GeoGebra 3D to visualize the part of a surface above or below a given region in the xy-plane so we can see what we're doing when we solve optimization problems for multivariable functions. We use a lot of features: graphing 3d functions, graphing planes, finding traces of a surface in a plane using the curve command, and graphing only part of a surface using an if command with conditions determined by the constraints. You definitely need to know that && is how we do an "and" for the constraints in the if command.
This is a great way to look at these sorts of problems in multivariable calculus.