# The Intermediate Value Theorem The intermediate value theorem states that **for all [[Function Discontinuities|continuous]] functions if two values $A$ and $C$ are part of the functions range, than all $B$ values that satisfy the inequality $A<B<C$ must also be part of the range.** The intermediate value theorem is useful for finding roots of continuous functions. If we find two points such that $f(a) < 0$ and $f(b) > 0$, per IVT we know that the function must have a zero between $a$ and $b$, as at some point it must cross the $x$ axis.