Is there a technical term for functions with $(-1)^n f^{(n)} \ge 0$ for all $n$?

Question

I have stumbled upon a class of smooth functions $f\colon [a,b] \to \mathbb{R}$ that satisfy $$(-1)^n f^{(n)} \ge 0$$ for all $n \in \mathbb{N}$. (Where $f^{(n)}$ denotes the $n$-th derivative of $f$). Is there a technical term for these kind of functions, so I can find out a bit more about them?

Answer 1

This is not quite what you have, but a function $f: (0, \infty) \to [0, \infty)$ with $(-1)^n f^{(n)} \ge 0$ is called completely monotone.