What exactly is your question? Lets say we want to find increasing intervals on . We apply the first derviative test. We do as you said, we find and set it equal to zero (lets say that is the zero). We then set up intervals based on the zeros (lets just say there is one for simplicity) so we should have something looking like . Now we pick two numbers, and we then find . If the value is positive that is an increasing interval and if it is negative it is decreasing. Does that make sense?