Mathematics:  This activity is appropriate for a calculus or analysis class. Students will investigate what it means for a curve to have slope. They will create a function which determines the slope of a curve f(x) at every point along the curve. They will identify this function as the first derivative, f '(x) and will express the first derivative as a limit statement.

Mathematical Thinking:  Students will look for patterns and make a generalization.

Technology:  The Geometer's Sketchpad 4.0.