Graphs of Derivatives - Discovery:
This three-page worksheet will guide your students to graph the derivative of a function and make observations about the following concepts:
* The slope of a tangent line to a curve can be identified at various points and used to create the graph of the derivative.
* The degree of f’(x) is equal to the degree of f(x) minus one.
* The second derivative of f(x) is denoted by f’’(x) and is the derivative of f’(x).
*The derivative of a cubic function is a quadratic function. The derivative of a linear function is a constant…etc.
Students can complete this activity even if they cannot yet differentiate. They must have some prior knowledge of parent functions and be familiar with the term "degree" of a function.
The questions are set up as a guided lab and students make discoveries in an inquiry style. They must answer critical thinking questions in complete sentences.
Students will need a straightedge.
Check out these other resources as well:
Factoring Polynomials "GridWords" : FULL SET
Systems of Equations: "Choose Your Own Journey" book