Google Classroom
GeoGebraGeoGebra Classroom

Lagrange visualizer

This will help you visualize what's happening with the Lagrange multipliers approach, and where the equation comes from. Input the objective function and the constraint function . C is the value of the constraint (if you pick wisely, you can leave C=0). The constraint curve is displayed in red. The slider c controls the level set , displayed in black. If red constraint curve crosses the black level curve, then moving along the constraint curve can take the value of f from below c to above c -- thus, the point of intersection is not a local extreme. So we are looking for points of tangency between the red and black curves. Move the slider c to achieve tangency; in doing so you will find the extreme values of constrained by . This is a 3D applet -- if you rotate the perspective, you can enable the graph of to see what's going on in 3D; but you should remember that we're really interested in the 2D picture.