Application of the Derivative

"Can calculus be used to figure out when a function takes on a local or a global maximum value? Absolutely. Not only that, but derivatives and second derivatives can also help us understand the shape of the function (whether they are concave upward or downward). If you have a basic conceptual understanding of derivatives, then you can start applying that knowledge here to identify critical points, extrema, inflection points and even to graph functions." quote from Khan Academy