Intermediate value theorem
Continuous function on an interval takes on every value between its values at the ends
Intermediate value theorem
In mathematical analysis, the intermediate value theorem states that if f {\displaystyle f} is a continuous function whose domain contains the interval [a, b] and s {\displaystyle s} is a number such that f ( a ) < s < f ( b ) {\displaystyle f(a)<s<f(b)} , then there exists some x {\displaystyle x} between a {\displaystyle a} and b {\displaystyle b} such that f ( x ) = s {\displaystyle f(x)=s} . That is, the image of a continuous function over an interval is itself an interval that contains f ( a ) , f...
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