Does the EVT apply

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.

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

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

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

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

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

• Whether they exist

• Their exact location

• Their continuity

• Their value