Numerical derivative explorer
- Warren Koepp
This is an online interactive version of the GeoGebra thing I did in class this week, where we put in a function y=f(x) on the interval [-5, 5] and plotted points on the graph of its derivative (i.e. y=f'(x)) numerically. To use it, put in a function for f(x), which will update on the plot in black. Drag the slider from left to right--this moves a point along your curve, recording the coordinates (x, f(x)) in the spreadsheet at 21 different locations along the curve, along with the slope at each point; and creating the point (x, slope at x) at each point. (The points don't update automatically when you change f(x); you have to drag the slider to update everything to your current function.) The red dotted line is the tangent to the curve at the point A(a, f(a)); the slider moves the value of "a" between -5 and 5, in steps of 1/2 unit. The green curve is whatever is in "candidate for derivative" box. If you compute f'(x) and want to see if you got it right, enter it in the box. If the green graph that results goes through all the points you generated when dragging the slider, then you got the derivative correct.
Please send me email and let me know what you like or don't like about this applet. Does it help you understand the concept of derivative, and instantaneous rate of change? Is it useful for checking your work in computing derivatives? Have you found a use for it other than what I wrote it for?