# What is the name for an increasing function that has an increasing or decreasing derivative, respectively

I often deal with some functions that are increasing, but where some are increasing less than linearly as a function of x, and others are increasing more than linearly. I would like to know the technical terms to describe such functions. Intuitively, the terms 'sub-linear' and 'super-linear' make sense to me to describe such functions, but evidently that is not correct terminology. It seems the term 'exponential' is often used loosely to refer to anything that is greater than linear, but I'm not sure about functions that are less than linear.

• How about "increasing concave function" or "increasing convex function"? – Joppy Oct 2 '17 at 8:13

If the derivative $f'$ of a function $f$ is increasing with $x$ then this function is called convex, and if $f'$ is decreasing then $f$ is called concave.