When using the Intermediate Value Theorem if ab then what happens?

Question

When using the Intermediate Value Theorem if a>b then what happens?

anonymous · Answer

Does that mean that f(a)=f(b) or that we are not able to prove that there exist any real zeros? These are not multiple choice options... I am just asking :).

blockcolder · Answer

You could just switch a and b around.
For example, if you had a=3 and b=-1, you could switch these two and let a=-1, b=3 so that a<b.

anonymous · Answer

Really? You could do that? Sounds a little weird... because I thought theorem's don't change...

blockcolder · Answer

The theorem goes:
$$\text{If a function}\ f(x)\ \text{is continuous on an interval}\ [a,b]\ \text{and differentiable}\
\text{on the interval}\ (a,b)\ \text{where }a<b, \text{then there exists a }c \in (a,b)\
\text{such that }f(c) \text{ is between } f(a) \text{ and }f(b).$$
So technically, since we are dealing with an interval, a<b always.

anonymous · Answer

Okay :). Thank You!

anonymous · Answer

I was just wondering, what if, I felt as if I saw somewhere that it wasn't...but I guess I was hallucinating or something.

blockcolder · Answer

You're welcome. =)