This tool allows you to input a function [i]f[/i]([i]x[/i]) (initially set as [i]x[/i][sup]2[/sup]), fix a base point B on its graph, and then see how moving a variable point A on the graph changes "h" (the horizontal distance between A and B) and the slope "m" of the [i]secant line[/i] connecting the two points.

Input your function in the indicated input box (if you want to explore a different function).[br]Use the slider to change the base point (B's) x-coordinate, i.e. x_0.[br]The point B is (x_0, f(x_0)); the red point A is at coordinates [br](x_0 + h, f(x_0 + h)). The value of "h" is displayed in blue, and the slope m of the segment connecting A and B is displayed in brown. The directed length "h" is illustrated by the blue segment on the x-axis. When A is to the left of B this h is negative; and it is positive when A is to the right of B.