Term for a function whose derivative is decreasing

Question

A "decreasing function" is one that gets smaller as its input gets larger. For example, f(x) = -x, f(x) = 1/x {x > 0}.

What can functions like sqrt(x), ln(x) be called? They are always increasing, but the rate at which they are increasing always slows down. Their first-order derivatives are decreasing functions.

ln(x) is a ____ function

Answer 1

Such a function is called a concave function. This is because it is concave downwards (convex side upwards). A concave function may decrease (although your examples do not) if the gradient/derivative decreases past zero.