/* [wxMaxima batch file version 1] [ DO NOT EDIT BY HAND! ]*/ /* [ Created with wxMaxima version 0.8.5 ] */ /* [wxMaxima: comment start ] Differentiability, first a zoom in to see locally linear [wxMaxima: comment end ] */ /* [wxMaxima: input start ] */ with_slider_draw3d( a, makelist(5*10^-(i/10),i,0,20), xlabel="x", ylabel="y", zlabel="z", surface_hide=true, enhanced3d=true, line_width=1, pic_width=700, pic_height=500, zrange=[-a,a], explicit((0.5*x+0.5*y+y^3+x^3)/(x^2+y^2+1), x,-a,a, y,-a,a)); /* [wxMaxima: input end ] */ /* [wxMaxima: comment start ] Not differentiable at the origin [wxMaxima: comment end ] */ /* [wxMaxima: input start ] */ draw3d(xlabel="x", ylabel="y", zlabel="z", surface_hide=true, enhanced3d=true, line_width=1, pic_width=700, pic_height=500, explicit(sqrt(x^2+y^2), x,-5,5, y,-5,5)); /* [wxMaxima: input end ] */ /* [wxMaxima: comment start ] Another not differentiable function but one whose partials exist. Not close to linear at any zoom level [wxMaxima: comment end ] */ /* [wxMaxima: input start ] */ with_slider_draw3d( a, makelist(5*10^-(i/10),i,0,20), xlabel="x", ylabel="y", zlabel="z", surface_hide=true, enhanced3d=true, line_width=1, pic_width=700, pic_height=500, zrange=[-a,a], explicit(x^2*y/(x^2+y^2), x,-a+0.000001,a, y,-a,a)); /* [wxMaxima: input end ] */ /* [wxMaxima: comment start ] Were it differentiable the following would go to zero as we approach the origin (it is the function divided by the distance to origin which is the difference between the function and the plane given by the partials) [wxMaxima: comment end ] */ /* [wxMaxima: input start ] */ draw3d(xlabel="x", ylabel="y", zlabel="z", surface_hide=true, enhanced3d=true, line_width=1, pic_width=700, pic_height=500, explicit(x^2*y/(x^2+y^2)^1.5, x,-5,5, y,-5,5)); /* [wxMaxima: input end ] */ /* Maxima can't load/batch files which end with a comment! */ "Created with wxMaxima"$