Lesson Plan: Increasing and Decreasing Intervals of a Function Using Derivatives Mathematics
This lesson plan includes the objectives, prerequisites, and exclusions of the lesson teaching students how to determine the increasing and decreasing intervals of functions using the first derivative of a function.
Objectives
Students will be able to
- formally define an increasing and decreasing interval of a function,
- determine the increasing and/or decreasing intervals for given function using the first derivative.
Prerequisites
Students should already be familiar with
- differentiation (including the chain, product, and quotient rules),
- finding first derivatives,
- increasing and decreasing functions,
- the concept of continuity (not necessarily the formal definition).
Exclusions
Students will not cover
- second derivatives,
- concavity,
- classifying critical points as local minima, maxima, or inflection points,
- graphical questions that do not require differentiation,
- stating whether a function is increasing or decreasing at a point.
