Critical Points and Absolute Values

Critical Points and Absolute Values

Assessment

Interactive Video

Created by

Thomas White

Mathematics

11th - 12th Grade

Hard

The video tutorial covers finding absolute maximums and minimums on closed intervals using the candidates test. It explains the Extreme Value Theorem, which states that every continuous function on a closed interval has an absolute maximum and minimum. The candidates test is used to determine these extrema at either endpoints or critical points. Two problem-solving examples are provided, one involving manual calculations and another using a calculator.

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14 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the primary focus of the video tutorial?

Finding absolute maximums and minimums on a closed interval

Learning about indefinite integrals

Finding relative maximums and minimums

Understanding open intervals

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What theorem is essential for finding absolute maximums and minimums on a closed interval?

Fundamental Theorem of Calculus

Extreme Value Theorem

Mean Value Theorem

Intermediate Value Theorem

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

According to the Extreme Value Theorem, what conditions must a function meet to have an absolute maximum and minimum?

The function must be decreasing

The function must be increasing

The function must be continuous on a closed interval

The function must be differentiable on an open interval

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Where must the maximum or minimum values occur according to the candidates test?

Only at the endpoints

At any point on the interval

At either an endpoint or a critical point

Only at critical points

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is a critical point in the context of the candidates test?

A point where the derivative is zero or undefined

A point where the function is decreasing

A point where the function is increasing

A point where the function is not defined

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

In the visual examples, what is shown about the absolute maximum and minimum?

They always occur at the endpoints

They can occur at critical points or endpoints

They are always equal

They do not exist on closed intervals

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the first step in solving a problem to find the absolute minimum of a function?

Find the indefinite integral

Calculate the derivative

Identify the endpoints and critical points

Determine the function's domain

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