Saturday, March 2, 2013

When the value of a function changes by a (perhaps) small amount delta x, there is a corresponding change delta y in the value of the function.  When the derivative of the function is known, the value of delta y can be approximated by value of dy, a value obtained by the tangent line approximation to the function at the point (a, f(a)).  This GeoGebra Worksheet enables the user to compare the values of delta y and dy for different points on the graph and different values of delta x.  By defining the settings of the graphic window in terms of delta x and delta y, the key aspects of the graph stay largely in place when the sliders are moved, so accurate comparisons between dy and delta y can more easily be made.