Finding Absolute Extrema of Functions

Finding Absolute Extrema of Functions

Assessment

Interactive Video

Mathematics

9th - 10th Grade

Hard

Created by

Thomas White

FREE Resource

The video tutorial explains how to find the absolute maximum and minimum values of a function on a closed interval. It begins with an introduction to the concept and proceeds with two examples. The first example involves finding critical points and evaluating the function at these points and the interval's endpoints. The process is reviewed, and a second example is provided to reinforce the learning. The tutorial emphasizes the importance of critical points and endpoint evaluations in determining absolute extrema.

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10 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the first step in finding the absolute maximum and minimum values of a function on a closed interval?

Evaluate the function at random points.

Find the critical points by taking the derivative.

Use a graphing calculator to find the values.

Guess the maximum and minimum values.

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

How do you determine the critical points of a function?

By setting the function equal to zero.

By finding where the derivative is zero or undefined.

By evaluating the function at the endpoints.

By graphing the function.

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What should you do after finding the critical points of a function?

Ignore them and focus on the endpoints.

Evaluate the function at these points and the endpoints.

Only evaluate the function at the endpoints.

Use a calculator to find the maximum and minimum.

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

In the first example, what is the absolute maximum value of the function on the interval?

16

-27/16

32

0

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the absolute minimum value of the function in the first example?

16

-27/16

32

0

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the purpose of evaluating the function at critical points and endpoints?

To find the average value of the function.

To determine the absolute maximum and minimum values.

To check if the function is continuous.

To find the derivative of the function.

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

In the second example, what are the critical points of the function?

x = 2 and x = -2

x = 1 and x = -1

x = 0 and x = 2

x = 3 and x = -3

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