Lesson: Curve Sketching using Derivatives Mathematics

In this lesson, we will learn how to use derivatives to graph different functions.

Lesson Plan

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.

Q1:

Consider the polynomial function whose graph is given below.

Use the given points and the fact that is a critical point of the function to determine .

Determine the intervals where .

Q2:

Which of the following is the graph of the function ?

Q3:

Which of the following is the graph of the function ?