The Second Derivative

As the point A is moved along the curve, the point D traces out the first derivative and the point E traces out the second derivative. Check boxes show the complete path of the first and second derivatives, respectively, along with the expression for the appropriate derivative. The general function that can be studied here is . The sliders control the values of the constants and hence the shape of the curve. The traces can be removed by adjusting the zoom on the frame. The reset button on the top right sets the curve back to the parabola.