Apply the EVT to the square function

Apply the EVT to the square function

Assessment

Interactive Video

Mathematics

11th Grade - University

Practice Problem

Hard

Created by

Wayground Content

FREE Resource

The video tutorial explains the importance of having a continuous function on a closed interval to ensure the presence of maximum and minimum values. It demonstrates how to identify these values by checking the endpoints, using the extreme value theorem. The tutorial also includes a graph analysis to visualize the function's behavior over the interval.

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5 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Why is it important for a function to be continuous on a closed interval?

To simplify integration

To make it easier to graph

To guarantee the existence of maximum and minimum values

To ensure it has a derivative

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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

Calculating the derivative

Checking the endpoints

Finding the inflection points

Determining the average value

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

According to the example, what are the minimum and maximum values identified?

(1, 1) and (2, 8)

(0, 3) and (3, 0)

(1, 0) and (3, 9)

(0, 0) and (3, 9)

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What does the Extreme Value Theorem ensure for a continuous function on a closed interval?

It is differentiable

It is integrable

It has both a maximum and a minimum value

It has a unique solution

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the significance of checking the graph of the function on the interval?

To find the derivative

To confirm the endpoints

To visualize the maximum and minimum points

To determine the slope

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