This is a demo that shows the tangent paraboloid to a point on a surface (x,y,f(x,y)), as an illustration of the second order taylor approximation in two dimensions. We expand f(x,y) as a Taylor series around the hotspot C, and drop all terms of order 3 or higher. To see that this is but an approximation of the surface, we look at surfaces that are the function graph of a function f(x,y) with degree {geq} 3. Note that for deg f = 2 or less, the second order taylor approximation is exact.