4-A. The Derivative Function

Instructions:
[list][*]Use the input box for f(x) to define a function. Use the input box and slider tool for c to move the point [math]P=(c,f(c))[/math] along the graph of the function. [/*][*]Use the "Estimate Slope" checkbox to show/hid a movable line segment. Click and drag the "move" point to estimate the tangent line at this point. Observe the point marked (x) on the right graph. Click the "Mark Point" button to leave a trace of this point. [/*][*]Repeat the above process at multiple points in the interval between a and b. This will generate several (estimated) points on the graph of the derivative function. [/*][*]Use the "Tangent" checkbox to show/hide the actual tangent line segment and trace the actual graph of the derivative function. [/*][/list]
4-A. The Derivative Function
The derivative function y = f'(x) is a [b]function [/b]whose outputs are the instantaneous rates of change of f(x) at each x value in its domain. This function has its own representations as a table, graph, or even a formula.

Information: 4-A. The Derivative Function