Intermediate Value Theorem Converse

[KF33]

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.

Homework Equations

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.

 

[Ray Vickson]

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.

Homework Equations

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?

 

[KF33]

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.