In mathematics, particularly in calculus, a stationary point or critical point is an input to a differentiable function where the derivative is zero (equivalently, the slope of the graph is zero): where the function "stops" increasing or decreasing (hence the name). For a differentiable function of several variables, a stationary or critical point is an input (one value for each variable) where all the partial derivatives are zero (equivalently, the gradient is zero.
For the graph of a function of one variable, this corresponds to a point on the graph where the tangent is parallel to the x-axis. For function of two variables, this corresponds to a point on the graph where the tangent plane is parallel to the xy plane.
The notion extends to differentiable maps from Rm into Rn and to differentiable maps between manifolds, but, in these case, only the term critical point (or sometimes bifurcation point) is used, not stationary point.
This article focuses only to the case of the functions of a single variable. For the other cases, see Critical point.