Twice Differentiable Function

Definition

A twice differentiable function is a function that has two continuous derivatives. This means that the function can be differentiated twice, and both of those derivatives are also continuous.

Related terms

First Derivative Test:

The first derivative test is used to determine whether critical points of a function correspond to local maxima or minima. It involves analyzing the sign changes of the first derivative around these points.

Hessian Matrix: The Hessian matrix is a square matrix of second-order partial derivatives of a multivariable function. It provides information about concavity and convexity at critical points.

Critical Points:

Critical points are values in the domain of a function where either the first derivative is zero or does not exist. They can correspond to local extrema or inflection points on the graph of the function.