Critical point
In chemistry, a critical point is the conditions (temperature, pressure) at which the liquid state of the matter ceases to exist. As a liquid is heated, its density decreases while the density of the vapor being formed increases. The liquid and vapor densities become closer and closer to each other until the critical temperature is reached where the two densities are equal and the liquid-gas line or phase boundary disappears.
In physics, it often also means the point of a second order phase transition.
In mathematics, a critical point (or critical number) is a point on the graph of a function where the derivative is either infinite, undefined, or equal to zero. The latter kind is a stationary point.
In higher dimensions, and for functions of several variables, this concept becomes a point where the rank of the derivative (Jacobian matrix) drops (see submersion).