Graphing Calculator -> Function Grapher -> Curvature

For 2D functions, Function Grapher has the ability of doing curvature related calculating and graphing. Following figure shows two circles of curvature at x=-3 and x=2.5 on the graph of function y=cos(x).

The curvature and the center of curvature can also be calculated. In this example, you can get the following results in Result Editor:

 Curvature circle:
     Position: x=-3, y=-.9899925
         Curvature: .9611386
         The radius of curvature circle: 1.040433
         Center of curvature circle: x=-3.145385, y=4.023233E-02
     Position: x=2.5, y=-.8011436
         Curvature: .5061505
         The radius of curvature circle: 1.975697
         Center of curvature circle: x=3.514582, y=.8941441

Graphing Calculator -> Function Grapher -> Curvature