Calculus › Using derivatives › critical number
critical number
Using derivatives
Conditions and Properties
A critical number of a function is a value in the domain of the function where the derivative is either zero or undefined. If a critical number is a point where the second derivative is not zero, then the function has a relative maximum at that point if the second derivative is negative, and a relative minimum if the second derivative is positive.
Applications
Critical numbers are essential in the analysis of functions as they represent points where the derivative is either zero or undefined, indicating potential locations for local maxima or minima. These values are crucial because they signal changes in the behavior of the function, such as transitions from increasing to decreasing or vice versa.