Does the EVT apply

Does the EVT apply

Assessment

Interactive Video

Mathematics

11th Grade - University

Hard

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The video tutorial discusses identifying function maxima and minima, emphasizing the need for continuity and closed intervals for the Extreme Value Theorem (EBT) to apply. It explains that while EBT ensures the existence of extrema, it does not specify their location, which can be at endpoints or within the function. The tutorial highlights that extrema are not always where the derivative is zero, stressing the importance of understanding these concepts.

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5 questions

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1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What are the two main constraints needed for the Extreme Value Theorem to apply?

Continuity and an open interval

Boundedness and a closed interval

Differentiability and an open interval

Continuity and a closed interval

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Why is it important for a function to be continuous when applying the EBT?

To ensure the function is periodic

To guarantee the function is bounded

To ensure the function is differentiable

To avoid undefined values within the interval

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is a necessary condition for the EBT to determine the existence of extrema?

The function must be periodic

The function must have a horizontal tangent

The function must be defined on an open interval

The function must be defined on a closed interval

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Where can the maximum and minimum values occur according to the EBT?

Only where the derivative is zero

Only at the endpoints of the interval

At the endpoints or within the interval

Only at points of discontinuity

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What does the EBT not specify about the extrema of a function?

Whether they exist

Their exact location

Their continuity

Their value