Derivatives have many mathematical applications. They can be used to find extrema, intervals of increasing/decreasing, inflection points, and concavity. Extrema are a fancy word for extreme values. This can either be minimum values (minima) or maximum values (maxima). Intervals of increasing/decreasing are the parts of a graph of a function in which it is going up or going down. Inflection points are points in which the concavity (bending) of a graph of function is changing. Concavity of a graph of a function can either be bending up (concave up) or bending down (concave down). Ultimately, the most important feature of differentiation is the optimization of a system. This deals with finding the most optimal constraints on a system.
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