There's a statement, that I believe is false
Between two distinct zeroes of a polynomial $p$, there is a number $c$ such that $p′(c) = 0$.
Here is my reasoning:
- A polynomial of an even degree has a derivative of an odd degree, so it has no root, in this case the theorem fails.
- The statement doesn't say that there's at least a number $c$.
Therefore, the statement fails. Is my thinking process correct?