Mathematics-Extreme Values

This section shows how to locate and identify extreme values of a continuous function from its derivative. Once we can do this, we can solve a variety of optimization problems in which we find the optimal (best) way to do something in a given situation at the points where ƒ has a minimum value, immediately to the left and immediately to the right. (If the point is an endpoint, there is only one side to consider.) Thus, the function is decreasing on the left of the minimum value and it is increasing on its right. Similarly, at the points where ƒ has a maximum value, immediately to the left and immediately to the right.