A function with $f^{\prime}(x) = 0$ for every $x$ in an interval is constant on the interval, as a consequence of the mean value theorem
Terms
| Term | This example | Why |
|---|---|---|
| corollary | ✓ | “A function with zero derivative on an interval is constant” is a corollary of the mean value theorem, because it follows by applying that theorem to two points of the interval. |
| conjecture | ✗ | “A function with zero derivative on an interval is not a conjecture, because it is proved. |