Twice Differentiable

Definition

A function is said to be twice differentiable if it has both a first and second derivative defined for all points in its domain.

Related terms

First Derivative Test:

A method used to analyze critical points of a function by examining intervals where the first derivative changes sign.

Taylor Series Expansion: An approximation technique that expresses functions as an infinite sum of terms involving their derivatives at a specific point.

Higher Order Derivatives: Refers to derivatives beyond the first and second order (third, fourth, etc.). They measure rates at which rates are changing.