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Which statements about the Extreme Value theorem are true? Check all that apply.

The extreme value theorem can apply to a piecewise function.
A continuous function can have a maximum value, but no minimum value, over a closed interval.
An extreme value of a continuous function can be at one of the endpoints of the given closed interval.
A quadratic function will always have its minimum and maximum values as the endpoints of a given closed interval.
Given the function f(x) = x2, the extreme value theorem guarantees the existence of a minimum and maximum value on the interval [−3, 4].

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Answer:

A. The extreme value theorem can apply to a piece wise function

C. An extreme value of a continuous function can be at one of the endpoints of the given closed interval

E. Given the function f(x)=x^2, the extreme value theorem guarantees the existence of a minimum and maximum value of the interval

I just took it on Edge and these were the correct answers !

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A. The extreme value theorem can apply to a piece wise function.

C. An extreme value of a continuous function can be at one of the endpoints of the given closed interval

E. Given the function [tex]f(x)=x^2[/tex], the extreme value theorem guarantees the existence of a minimum and maximum value of the interval [tex][-3, 4].[/tex]

Extreme Value theorem:

  • If a function f(x) is continuous on a closed interval [a, b], then f(x) has both a maximum and a minimum on [a, b].
  • If f(x) has an extremum on an open interval (a, b), then the extremum occurs at a critical point.

We know a piecewise function is a function that is defined on a sequence of intervals.

So, we can say that an extreme value of a continuous function can be at one of the endpoints of the given closed interval and the extreme value theorem can apply to a piecewise function.

For the function [tex]f(x) = x^2,[/tex]

[tex]f'(x) =2x \\f'(x) =0\\2x=0\\x=0\\[/tex]

Which lies in the interval [−3, 4].

So the correct statements are:

The extreme value theorem can apply to a piecewise function.

An extreme value of a continuous function can be at one of the endpoints of the given closed interval.

Given the function [tex]f(x) = x^2,[/tex] the extreme value theorem guarantees the existence of a minimum and maximum value on the interval [tex][-3, 4].[/tex]

Learn more:https://brainly.com/question/23137504

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