Function/Algorithm that Returns Number of Roots within an Interval

Question

Let $f(x)$ be a (non-polynomial) function that is continuous and differentiable within an interval $[a,b]$ and has a finite amount of simple roots in that interval. Is there a function $g(a,b)$ or algorithm that will return the number of real roots in that interval? It will be sufficient for the algorithm to tell me if a root exists in that interval or not.