You may use the applet to locate, by moving the little circle on the parabola, the extrema of the objective function [math]f(x,y)=x^2+y^2[/math] along the constraint curve [math]g(x,y)=y^2-x=5[/math]. According to the method of Lagrange multipliers, an extreme value exists wherever the normal vector to the (green) level curves of [math]f(x,y)[/math] and the normal vector to the (blue) constraint curve are parallel (or coincide on the graph).