# Intermediate Value Theorem Converse

## Homework Statement

I was given the problem of determining if the Converse of the Intermediate Value Theorem in my book was true. Below is my theorem from the book.

## The Attempt at a Solution

I had looked at the converse and tried to draw some examples, and I am thinking it is false. I am leaning that way, because technically the function may or may not be continuous. I just need to know if I am on the right direction.

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## Homework Statement

I was given the problem of determining if the Converse of the Intermediate Value Theorem in my book was true. Below is my theorem from the book.

## The Attempt at a Solution

I had looked at the converse and tried to draw some examples, and I am thinking it is false. I am leaning that way, because technically the function may or may not be continuous. I just need to know if I am on the right direction.
What, exactly, would be the converse of the intermediate-value theorem?

What, exactly, would be the converse of the intermediate-value theorem?
If there is at least one number c in [a,b] such that f(c)=k, then f is continuous on the closed interval [a,b] and k is any number between f(a) and f(b). I got the answer though I think.