Hence we have seen that if {{MATH_538}} is zero at a point and increasing on an interval containing that point, then {{MATH_539}} has a local minimum at the point. If {{MATH_540}} is zero at a point and decreasing on an interval containing that point, then {{MATH_541}} has a local maximum at the point. Thus, we see that we can gain information about {{MATH_542}} by studying how {{MATH_543}} changes. This leads us to our next section.