Extremal Points, Critical Points, and Saddle Points of Analytic Functions.

The article examines the relation among critical points, external points, and saddle points of a complex analytic function. It also presents aspect of function theory in mathematics. It is reported that the familiar relation between local extremal points and critical points for realvalued functions does not hold analytic functions. It is stated that a nonconstant analytic function has no local extremal points other than its zeros. The contour integral can be evaluated using the residue theorem in many mathematical cases.