I am right now studying linear and non-linear optimizations while attending a mandatory mathematics course @ Universität in Hagen. Functions from R^2 -> R can be easily visualized - guess that qualifies for a textbook example

... Consider this optimization problem
The visualization contained in the course textbook looks like this
This is a
contour plot - but I don't think its helpful to just present this graph. The normal plot and the contour graph made things a lot easier for me - I fired up the
XMaxima CAS, and plotted this graph and it's contour graph
From an educational and visual point of view I think it's obvious which one is easier to grasp for a student ...