- A property of a function. A differentiable function is said to be concave (sometimes 'concave downwards') if, in comparing two points, a and b, the first derivative is falling. Thus, in the figure, the function relating health to utility is concave, implying that additional equal increments of health have a decreasing marginal utility to whoever is assessing their utility. A function may be convex (or concave upward) when the reverse applies. It may also be initially concave and then convex (or vice versa), when the point at which the change occurs is termed the 'point of inflexion'.