Introduction:

Mean value theorem (also known as intermediate value theorem) is one of the properties of continuous functions on closed intervals, and it is also one of the important properties of continuous functions on closed intervals.

In mathematical analysis, the intermediate value theorem shows that if the domain is a continuous function f of [a, b], then at a certain point in the interval, it can take any value between f(a) and f(b), that is, the function value in an interval where the intermediate value theorem is a continuous function must be between the maximum value and the minimum value.

Intermediate value theorem, also known as intermediate value theorem, is one of the properties of continuous function on closed interval and one of the important properties of continuous function on closed interval. In mathematical analysis, the intermediate value theorem shows that.

If the domain is the continuous function f of [a, b], then at a certain point in the interval, it can take any value between f(a) and f(b), that is, the intermediate value theorem is that the function value in an interval of continuous function must be between the maximum and minimum.

There is an important corollary: If a continuous function has opposite sign values in the interval, then it has roots in the interval (bolzano's theorem).