A brief example of tracing a point on its function and simultaneously mapping the derivative at that point.

Point A is on the graph, and moves along the graph as you graph it. Point B is the derivative at point A. Notice when the line has a positive slope that the derivative is positive (above the x-axis). Notice when the line has a 0 slope (max or min) that the derivative (point B) is 0. Notice that when the graph has a negative slope (falling from left to right) that the derivative is negative (below the x-axis).