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

  • 1
    It might be better to ask this question on a maths stack. Off hand, I don't think that there is a specific term.
    – Mick
    Nov 15, 2022 at 0:47

1 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.

  • 1
    I’ve also heard concave down and concave up.
    – Jim
    Nov 15, 2022 at 2:48

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