In this demonstration you may type in a function f(x) in the control panel. This function appears in the window titled "Graph: f(x)". Along the x-axis, slide the red hotspots to choose points x₀ and x₀ + h. The demonstration shows the area under f(x) for this interval in yellow and the approximating rectangle in green. If F(x) is the corresponding area function of f(x), as defined above, then the yellow area is equal to F(x₀ + h) - F(x₀). Meanwhile, the area of the rectangle is equal to h f(x₀). These two areas are calculated and displayed in the control panel. Notice that as you make h smaller, the yellow area and the area of the rectangle approach each other. The second graph window plots the area function F(x). Two vectors are drawn at F(x₀): the orange vector is (h, F(x₀ + h) - F(x₀)) while the cyan vector is (h, h f(x₀)). We know that as h get smaller and smaller the slope of the orange vector approaches F'(x). Notice that the slope of the orange vector also approaches the slope of the cyan vector, which is f(x).