Contour plots

A contour plot is a 2-dimensional way to visualize a 3-dimensional surface. It is done by by plotting constant z slices, called contours (a.k.a. level sets). That is, given a value for , points/lines/curves are drawn for the coordinates where that value occurs.

Near a minimum

This is the contour plot for the function near . Noticing the closed contour lines with lower values in the center and higher values on the outside.

Near a maximum

This is the contour plot for the function near . Noticing the closed contour lines with higher values in the center and lower values on the outside.

Near a saddle point

This is the contour plot for the function near which is a saddle point.