This applet is designed to help students
develop a visual intuition about the tangent line as a limit of secant
Click on the button below to launch the
The applet has a control window and 2 graphics windows.
The f(x) window shows a graph of the function in green.
There is a red dot on the graph and on the x-axis. The
dot on the axis is the hotspot and determines where we zoom in.
The hot spot can be dragged back and forth.
The yellow dot is at the red dot plus delta. The value of
delta can be controlled from the control panel.
The blue secant line connects the red and yellow dot. The
slope of the secant line is displayed on the control panel.
The magenta patch on the axis and graph is centered at the hot
spot with a radius of delta.
You have the option of displaying the tangent line in orange.
The close up window zooms in on the hot spot plus or minus
delta. Notice how when delta is small the tangent and secant
lines coincide. (It is also worth noticing that when delta gets
small enough, the graph of the function looks like a straight line that
coincides with the tangent line.)
Things to notice:
<>For a given point on the function, how small should delta be
the secant to be a good approximation of the tangent? Does this
depend on the hot spot chosen?