I use this worksheet as an introduction to the second derivative test. Students use the graphing calculator to generate the graphs of both a function and it's second derivative. They do not need to calculate the derivative at this point so the calculator comes in handy for the graphing.

Students observe and record the behavior of the graph of the derivative, thus discovering for themselves how the behavior relates to the original function. They can work alone or in pairs - my preference is for them to work in pairs so they can discuss their findings.