For a function of one variable, a critical point is a point at which the derivative is zero (at which the tangent is horizontal).

The concept of critical points in the dynamic, as used in power cycle theory, refers to (1) critical points on the relative power curve itself, and (2) critical points on the curve of the dynamic of change in relative power, that is, on the curve of the rate of change in relative power. Hence, the critical points in the dynamic are (1) the maximum and minimum of the relative power curve itself, and (2) the points of inflection on the relative power curve, since these are the maximum and minimum of the curve of the first derivative.

Likewise, inflection point is as defined in both calculus and differential geometry. The calculus definition stems from calculus of variations and differential manifolds theory: the second derivative is zero (note that the first derivative is not required to be zero, which is a special case of inflection point of importance in catastrophe theory) (Bronshtein and Semendyayev 1985, pp. 242–8). The differential geometry definition (pp. 554–55) is based on curvature conditions, namely, that the curvature changes sign at the point of inflection. A few algebraic steps show that the curvature condition required at the inflection point occurs for the general asymmetric logistic precisely when the second derivative is zero.