The purpose of this applet is for you to practice sketching derivative functions using slopes of tangents to the function.
Use the slopes of the tangent lines on the original function f to sketch the first derivative f ' on your own graph paper.
Then use the slopes of the tangent lines on the first derivative f ' to sketch the second derivative f ''. Remember that
the y-values on the derivative graph match the slopes of the tangent lines.
When ready, click the check boxes in succession to gradually reveal the graphs of f ' and f '' to check the accuracy of
your sketches. Randomly generate a new set of functions by clicking the blue arrows in the top right corner.

Where are there horizontal tangent lines? What does this mean for the y-values on the derivative function?
Where is the function increasing, and what can we say about the slopes of the tangents at these points?
Where is the function decreasing, and what can we say about the slopes of the tangents at these points?