Students will be able to
- identify the graph of a given polynomial or rational function by considering the derivative of the function,
- use local extrema and intervals of increase and decrease to help sketch the graph of a function,
- use the second derivative, points of inflection, and concavity of a polynomial or rational function to help sketch the graph of a function.
Students should already be familiar with
- differentiating polynomial functions and rational functions,
- finding and identifying the critical points of a function using the first and second derivatives of that function,
- finding the intervals of increase and decrease of a function,
- finding the points of inflection of a function,
- finding the concavity of a curve along different sections of it.
Students will not cover
- graphing functions other than polynomial or rational functions using derivatives.