Intuitive Derivative Graphing Exercise

Below, the graph of a function is shown. The LIGHT GREEN POINTS control the appearance of the entire graph. So to start & during this exercise, please don't touch these. The ORANGE POINTS are points that lie on the graph of this function. These points can be dragged anywhere you like on the curve prior to or during your completion of this exercise. The Y-COORDINATE of each WHITE POINT is the same as the slope of the segment passing through (either the light green or orange) point directly above it or directly below it. Given this information, position the WHITE POINTS in such a way that it causes the segment above it or below it to appear tangent to the graph of the function. By doing so, you will be finding a possible point on the graph of the derivative of this function. When you're done positioning the white points, use the pen Toolbar Image tool to sketch the derivative graph based upon your work. To check your work, click the "Check Your Work" checkbox.


If you would like to try this exercise multiple times, simply use the delete icon Toolbar Image to erase any previous sketches you made. Then, reposition any one (or more) of the four green points to get an entirely different graph. Just be sure not to move any green points in the middle of an exercise, at it will change the graph of the entire function. Note: If you do move any of the light green points and the function graph disappears, simply refresh the page in your browser.

Quick (Silent) Demo