Here you have a function that can be adjusted with the dots. Then you have a begin point and an end point that can be moved on the [math]x[/math] axis. The net change in [math]y[/math] from beginning to end is in the shaded area. A green shade indicates positive change, and a pink shade indicates negative change.[br]The point "Now" can be moved to see how the change in y acts as the "Now" position changes. The slope is shown with the brown triangle. Observe how the change in [math]y[/math] varies with a change in [math]x[/math] relative to the height of the triangle.

The net change in a function [math]F\left(x\right)[/math] over an interval [math]a\le x\le b[/math] is the integral of its rate of change:[br][math]F\left(b\right)-F\left(a\right)=\int_a^bF'\left(x\right)dx[/math][br][br]The restriction is that F(x) must be Lipschitz continuous and differentiable on the closed