Our current unit in calculus involves a lot of curve sketching of rational functions (a PITA if you ask me).

Part of this process involves us doing derivative tests to find the intervals of increase/decrease (1st deriv) and concavity (2nd deriv)

I'm wondering if there is a way to easily predict the positive/negative intervals of a (rational) derivative function in every case?

I'm getting tired of sticking the function in my calculator and finding values...

-C