Calculus - Definition of a Derivative - Using the Rule of 4

This activity incorporates the graphing calculator to help students understand the definition of a derivative. Students in AP Calculus and Calculus should be studying the concepts in Calculus graphically, numerically, verbally and analytically ( which is also known as the rule of 4).

This activity sheet will help develop the student’s conceptual understanding of the definition of a derivative in these four ways:

• Students create graphs and tables of a function and a difference quotient. As they change the difference quotient so two points on the graph approach each other, the difference approaches the derivative of the function. Students are asked to describe what they see happening in the table and the graph. Students develop the formula for a derivative based upon what they see happening in the table and graph.

• In the lesson students study two different functions: y = x^2 and y = x^3. • After students have worked through the lesson on the two functions they, then are given eight additional functions to study.

Comments from Buyers:

• I used this last year and my students loved it! It really helped them to understand what a derivative is.

• Well organized. I would have liked it if the individual steps had numbers or letters rather than bullet points, but it did a nice job developing the theme.