This demo shows the tangent planes for the monkey saddle Ax³ - 3Bxy². Note that the intersection set of the tangent plane with the function graph allows us to classif_y the points of the surface into two categories: for some points in the domain, the tangent plane meets a neighborhood of the point (x₀,y₀,f(x₀,y₀) on the graph in a single point, whereas for other points, the tangent plane meets the graph in a pair of curves, or occasionally in a more complicated set of points.