Lesson: Extrema of a Function Graph Mathematics • 10th Grade

In this lesson, we will learn how to interpret the minimum and maximum values and the end behavior of a function graph.

Lesson Plan

Students will be able to

identify local and global maxima and minima of functions from their graphs,
make deductions about the properties of a function by investigating its end behavior.

Lesson Worksheet

Q1:

Find the maximum or minimum value of the function , given .

Q2:

Consider the graph of the quartic shown.

Which of the points , , and is a local maximum?

Which of the points , , and is a local minimum?

Which of the points , , and is a global minimum?

By considering the end behavior of the quartic, determine whether the leading coefficient is positive or negative.

Q3:

Consider the cubic graph shown.

What are the coordinates of the local maximum?

What are the coordinates of the local minimum?

If we consider the end behavior of this cubic, it enters into the bottom left quadrant and exits from the top right quadrant. Is the leading coefficient of this cubic positive or negative?