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AP Calculus AB/BC
When the first derivative of a function changes from positive to negative at a specific point, it means that the slope of the function is decreasing as we move towards that point.
A local maximum occurs when a function reaches its highest value in a particular interval but may not be the absolute maximum over its entire domain.
An inflection point is where the concavity of a curve changes. It occurs when the second derivative changes sign.
A critical point is where either the first derivative does not exist or is zero. It can correspond to local extrema or points of inflection.