Tangents and Normals

This excel file explores the relationship between tangents and normals.

In the first interactive sheet the user can alter the coefficients of a quadratic function and see how this affects the graph and equation of both the tangent and normal at a changeable point, P. The following interactive sheet repeats this for a cubic function.

The third sheet looks at the area of the triangle bounded by the x- and y-axis and the tangent for a cubic function. The next sheet finds the area bounded by the axes and the normal. Again the values of the coefficients can be adjusted and the effects observed.

The final interactive sheet investigates the coordinates at which the tangent at point P intersects with the cubic at a second point, Q. The equation of the tangent and the coordinates of point Q can be shown.

Note
This program was designed by be viewed on a screen with a resolution of 1024 x 768. Users may have to adjust the resolution of their screen for the pages to display as was originally intended. The program uses macros which need to be enabled on users’ machine.