Math 3 Winter 2004

Introduction to Calculus

Class Demo for the Implicit Differentiation

January 23, 2004

>	with(plots):

Warning, the name changecoords has been redefined

   Plotting implicity defined functions is not easy

>	f := (x, y) -> x^2 + y^2:

>	implicitplot(f = 25, -5 .. 5, -5 .. 5);

    Descartes's Folium

>	f := (x, y) -> x^3 + y^3 - 6*x*y;

>	implicitplot(f = 0, -5 .. 5, -5 .. 5, thickness = 2);

    Tangent line at (3, 3) is
    Tangent line at (4/3, 8/3) is
    Tangent line at (2^(4/3), 2^(5/3)) is

>	display(implicitplot(f = 0, -6..6, -6..6, thickness = 2, grid = [50, 50]), plot({6 - x, 4*x/5 + 8/5, 2^(5/3)}, x = -6..6, y = -6..6, color=blue));

    Tougher example

>	f := (x, y) -> 2*y^3 + y^2 - y^5 - x^4 + 2*x^3 - x^2;

>	implicitplot(f = 0, -1..2, -2..2, thickness = 2, grid = [70, 70]);

    Look more carefully

>	implicitplot(f = 0, -0.5..1.5, 1.5..1.7, thickness = 2, grid = [50, 50]);

>