Lesson: Minimum and Maximum Values of a Graph

In this lesson, we will learn how to interpret the extrema and the end behavior of a given graph.

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Worksheet: Minimum and Maximum Values of a Graph • 6 Questions • 2 Videos

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?

Q4:

What is the maximum value of the function ?

Q5:

Consider a function , where , , and are integers larger than 1. Which of the following statements is true?

Q6:

Which of the following has the lowest minimum value?

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