Stationary Point

Definition of stationary point from wikipedia :

In mathematics, particularly in calculus, a stationary point or critical point of a differentiable function of one variable is a point on the graph of the function where the function’s derivative is zero. Informally, it is a point where the function “stops” increasing or decreasing (hence the name).

 

Lagrange multiplier helps us to find all the stationary points, It can be local minima, local maxima, global minima or global maxima. Once we evaluate objective function at each of these stationary point we can classify which one is local/global minima and maxima.

 

Example