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A critical point is a point on a function where the derivative is either zero or undefined. It represents a potential maximum, minimum, or inflection point.
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A local maximum is a critical point where the function reaches its highest value within a small interval around that point.
A local minimum is a critical point where the function reaches its lowest value within a small interval around that point.
An inflection point is a critical point where the concavity of the function changes from upward to downward or vice versa.