Calculate slopes of secant lines, create tangent lines with the same slope, and note observations about the functions and slopes.

• Calculate slopes of secant lines, create tangent lines with the same slope, and note observations about the functions and slopes

Students will find the slope of a given secant line and a tangent line they place on the graph of a function and try to get their slopes to match. Students should see that the tangent and secant lines are parallel and make a connection leading to the Mean Value Theorem for Derivatives. Following a counterexample, students will also explore Rolle’s Theorem.