What does twice differentiable mean?
Understand the Problem
The question is asking for the definition of the term 'twice differentiable' in the context of mathematics. It seeks an explanation of what it means for a function to have derivatives that can be taken twice, indicating certain properties of the function's smoothness.
Answer
A twice differentiable function has a continuous second derivative.
A twice differentiable function is a function that has a second derivative, meaning you can differentiate its first derivative, and this second derivative is also continuous.
Answer for screen readers
A twice differentiable function is a function that has a second derivative, meaning you can differentiate its first derivative, and this second derivative is also continuous.
More Information
This property is often essential for determining the curvature of a function and in optimizing functions to find maxima and minima.
Tips
Confusing differentiability with continuity; ensure both derivatives are continuous.
Sources
- What does a twice differentiable function mean? - math.stackexchange.com
- Twice Differentiable Function - Vocab, Definition, and Must Know Facts - library.fiveable.me
- Twice differentiable - Calculus - Math Open Reference - mathopenref.com
