Concavity refers to the curvature of a function that indicates whether it opens upward or downward. In optimization, understanding concavity is crucial for determining the nature of critical points, which helps in identifying whether they represent maximum or minimum values of a function. The concavity of a function is assessed using the second derivative test, where a positive second derivative indicates concave up (local minimum) and a negative second derivative indicates concave down (local maximum).
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