Derivatives and Tangent Lines

This applet is designed to build the intuition between the idea of a derivative being the slope of the line tangent to a curve and the idea of a derivative as a function symbolically computed form the formula of the original function.

The main viewing window gives the graph of a function f(x), a point T, the tangent line at a the point T, and a point with that turns the slope into the height of a point.  The main viewing window also graphs a guessed derivative for the function.
Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and activated. (click here to install Java now)
f(x) = dfdxGuess(x) =
Min X = Max X = Min Y = Max Y =

The applet opens using the function f(x)=x^2/6 - 2x + 4.

Drag the point T so that it has an x value of 12 and record the slope.  Do the same for x values of 9 and 6.
Make a guess at the formula for the derivative.

Type in your guess, hit  enter and check if your guessed derivative is correct.  (If correct, the graph of the guess will be covered with the trace of the slope point.)
Type in a new f(x) and try again.  To remove the trace, reset the x value of T.

Created with GeoGebra

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Last updated By Mike May, S.J., August 11, 2007.