# 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.