Derivatives and Tangent Lines
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.
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
Return to the
Applets for courses below calculus page.
Return to the Calculus
Return to the GeoGebra Applet page.
Last updated By Mike May, S.J.,
August 11, 2007.