In calculus, local maximums and minimums are points on a graph where the function reaches its highest or lowest value within a small neighborhood, respectively. They occur where the slope of the function (its derivative) is zero. At a local maximum, the function is increasing on one side of the point and decreasing on the other side, indicating a change from positive to negative slope. Conversely, at a local minimum, the function is decreasing on one side and increasing on the other, showing a c