Net Change Theorem


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 axis. The net change in from beginning to end is in the shaded area. A green shade indicates positive change, and a pink shade indicates negative change. 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 varies with a change in relative to the height of the triangle.

The Net Change Theorem

The net change in a function over an interval is the integral of its rate of change: The restriction is that F(x) must be Lipschitz continuous and differentiable on the closed