Lesson Plan: Curve Sketching using Derivatives Mathematics
This lesson plan includes the objectives, prerequisites, and exclusions of the lesson teaching students how to use derivatives to graph a function.
Objectives
Students will be able to
- identify the graph of a given 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 limits to find vertical and horizontal asymptotes of the graph of a function and its end behavior,
- use the second derivative, points of inflection, and concavity of a polynomial or rational function to help sketch the graph of a function.
Prerequisites
Students should already be familiar with
- using chain,product, and quotient rule to differentiate 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.
Exclusions
Students will not cover
- oblique asymptotes.
