Name: Rain Xia       Student Number: 59118159

Intermediate Value Theorem

In a continuous function, there is an interval [a,b] in x-axis, the corresponding y value of a and b is f(a) and f(b). There has a point c in x-axis which is bigger than a and smaller than b, and f(c) is between the values of f(a) and f(b) definitely. It is called Intermediate Value Theorem.

For example, when a<0 and b>0, there must has a point c which equals to 0 if a<c<b. It has the same idea of the previous one.

The Intermediate Value Theorem must in a continuous function, the function is continuous in [a,b]. If the function is not continuity, the Intermediate Value Theorem is not true anymore.