# Rolles Theorem

1. Nov 7, 2011

### Miike012

The first hypothesis is that f is continuous on [a,b]....

Is there a more concise mathematical way of saying... "because the function f is a polynomial it is continuous in its domain."? Because I rather not write that on my test it looks sloppy and non professional...

2. Nov 7, 2011

### Staff: Mentor

I don't see any problem with what you said. All polynomials are defined and continuous on the entire real line.

3. Nov 7, 2011

### Miike012

I know but is there another way to state that using math symbols or something to make it more concise in like 2-5 words.

4. Nov 7, 2011

### Staff: Mentor

This is all you need to say.
"...because the function f is a polynomial, it is defined and continuous [STRIKE]in its domain[/STRIKE] on the entire real line."

5. Nov 7, 2011

### LCKurtz

Assuming you are using standard notation: "If p is a polynomial, then p ε C[a,b]".

6. Nov 8, 2011

### HallsofIvy

Staff Emeritus
Note, by the way, that Rolle's theorem also requires that the function be differentiable on some interval. Fortunately, it is also true that all polynomials are differentiable for all x.