ABSTRACT
This chapter looks at the ways to locate the minima and maxima of a given function. Any continuous function on a compact set has a global minimum and a global maximum. This is where derivative information becomes useful. One does not need differentiability really as convexity is enough to local minima, but the provision of a derivative gives us extra tools. A likely place for an extreme value is where the tangent line is flat. A function can have a minimum or maximum at a point where the functions has a corner or a cusp — in general where the function’s derivative fails to exist. Finally, if the function is defined on a closed interval, the function could have extreme behavior at an endpoint. These types of points are called critical points of the function. The chapter describes some cooling models. Newton formulated a law of cooling by observing how the temperature of a hot object cooled.
