This activity will walk students through investigations of the value of the slope of a tangent line to polynomial curves at various points. An instantaneous scatter plot will be generated so that the students will discover that they can not only investigate derivatives of various polynomials, but that the derivatives themselves are in fact functions, also something that many students don't catch on to right away when beginning Calculus.
Before the Activity
Students are expected to have just finished learning limit definition of a derivative and other prerequisite limit skills, including evaluating the limit definition of a derivative for simple functions like x^2 and x^3. Additionally, the students are expected to know that the slope of a tangent line to a curve at a point is equivalent to the value of a derivative of the function at that point.