What is "stationary point"

n. (context mathematics English) A point on a curve where the gradient is zero. This point can be a maximum, a minimum, or a point of inflection.

In mathematics, particularly in calculus, a stationary point or critical point of a differentiable function of one variable is a point of the domain of the function where the derivative is zero (equivalently, the slope of the graph at that point is zero). Informally, it is a point where the function "stops" increasing or decreasing (hence the name).

For a differentiable function of several real variables, a stationary (critical) point is an input (one value for each variable) where all its partial derivatives are zero (equivalently, the gradient is zero).

Stationary points are easy to visualize on the graph of a function of one variable: they correspond to the points on the graph where the tangent is horizontal (i.e., parallel to the -axis). For a function of two variables, they correspond to the points on the graph where the tangent plane is parallel to the plane.