The two conditions of the theorem are, 1. The function f(x) is continuous in the interval [a, b], and of course all basic elementary functions can be satisfied.
2 . f(a)f(b)& lt； 0,
Note that the conclusion is that f(x) has at least one zero above the interval (a, b).
Notice the difference? Is the change above the interval. The former is a closed interval and the latter is an open interval. If they can be equal, is it inconsistent that the endpoints are exactly equal to 0? Forget to think twice.
Besides, can't the former be a closed interval? Obviously not, such as piecewise function, it is easy to give counterexamples.
Good luck ~ _ ~