Problem:
Explore the construction of the tangent line as the limit of secant lines at various points of the graph of the function

f(x) = x3 - 4 x + 1.


Visualization:
The following LiveMath Notebook gives an animation of the construction of the tangent line as the limit of secant lines at the point (a,f(a)). The point (a,f(a)) is the yellow point on the graph and the point (a + h,f(a + h)) is the green point on the graph.

The value of h appears in the upper right-hand corner of the graph.

You can start and stop the animation by clicking on the graph.

You can change the value of a and the equation of f. View an animation to see how this can be done. In addition, you can change the speed of the animation by clicking on the expression 4 frames/second which is just below the graph.