Secant Lines and Tangent Lines

Click this button to open a window where you can experiment with secant lines and tangent lines. A tangent line and a secant line to a curve are shown. You can drag the endpoints of the line. The slopes of the tangent and secant lines are displayed. Note that to get a visual estimate of the slope, it's a good idea to hit the "Equalize Axes" button, which will make sure that the same scale of length is used on both coordinate axes. You can select examples from the pop-up menu at the top of the applet, or you can type in your own functions. Use the right mouse button to drag the graph.

Functions and Their Derivatives

Click the button to open a window that shows a graph of a function along with the graph of its derivative. The formula for the derivative is shown at the bottom of the window. A tangent line to the original function is shown, and the corresponding point on the graph of the derivative is marked with a small crosshair. You can move the point of tangency by adjusting the scroll bar at the bottom of the window, or you can type in the x-coordinate of the point. Select examples from the pop-up menu at the top of the window, or enter your own function. Use the right-mouse button to drag the graphs around. Use the left-mouse button to zoom in and out: To zoom in, click the graph with the left mouse button, or click and drag to draw a rectangle around the region that you want to zoom in on. If you want to zoom out, hold down the shift key while you use the left mouse button.