IVT
Units & Measurements abbreviation · Math
| Stands for | Intermediate value theorem |
|---|---|
| Categories | Units & Measurements |
IVT stands for Intermediate value theorem, a math abbreviation.
A calculus theorem stating that a continuous function on a closed interval takes every value between its endpoint values. If f(1) < 0 < f(2), then f has a root between 1 and 2.
Example: By the IVT, x³ − x − 1 has a root between 1 and 2, since f(1) = −1 and f(2) = 5.
Usage notes
The IVT justifies the bisection method for finding roots numerically. Continuity is essential, since a function with a jump can skip values. Bernard Bolzano gave an early rigorous proof in 1817. A playful consequence is that some pair of opposite points on the equator always has the same temperature.