A Very Bumpy Wave

A Very Bumpy Wave. Here, you can use the slider to change the values of k, which determines the height of the horizontal plane intersecting the surface. As you change k, the intersection of the plane and the surface show you the level curves. What difference is there in the nature of the level curves when k is approaching a local max or local min vs. when k is approaching a saddle point? For any value of k, you can right click and drag the 3D graph to get a better view.