Concave downward

In mathematics, a concave function is the negative of a convex function. A concave function is also synonymously called concave downwards, concave down, convex upwards, convex cap or upper convex.

A real-valued function ${\displaystyle f}$ on an interval (or, more generally, a convex set in vector space) is said to be concave if, for any ${\displaystyle x}$ and ${\displaystyle y}$ in the interval and for any ${\displaystyle \alpha \in [0,1]}$,

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