Excerpt from the Function of a Complex Variable

Abstract

The need to derive a function arose while trying to find a universal way to determine the tangent of a curve in geometry and velocity in mechanics. In mathematical analysis, in a branch of mathematics, a derivative is a measure of how (how fast) a function changes its values when its input values change. The derivative of the curve at a point represents the coefficient of the direction of the tangent of a given curve at that point. Derivations are a useful tool for examining graph functions. All points within the domain of real functions that represent local extremes have zero for the first derivative. However, not all critical points are local extremes; for example f(x) = x³ has a critical point at x = 0, but has neither a local maximum nor a local minimum at this point.