A function is concave if:
A) its slope is always nondecreasing
B) a line drawn connecting two points on the curve never lies below the curve
C) its slope is always nonincreasing
D) it is always positive

Question

A function is concave if:
A) its slope is always nondecreasing 
B) a line drawn connecting two points on the curve never lies below the curve 
C) its slope is always nonincreasing 
D) it is always positive

Quizplus · Accepted Answer

A function is concave if its slope is always nonincreasing. In other words, as we move from left to right along the function, its slope decreases or stays the same. This means that the function is "curving inward" and any line drawn connecting two points on the curve will lie above the curve. Choice (B) describes a convex function, not a concave function. Choice (A) and (D) are incorrect as they are not true for concave functions.

A Function Is Concave If