Graphically explore the linear approximation of the function

y = f(x) = x3 - 5x + 6

using the tangent line at x = a for various values of a.

Use the following Mathview Notebook which begins with the tangent line at x = a = 1 to zoom in at the point (1, 2) to see how well the graph of the tangent line approximates the graph of f. You can change the value of a and the function f. View an animation to see how this can be done.