# How does the first derivative test work?

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The first derivative test is a method used to analyze critical points of a function to determine whether they correspond to local maxima, local minima, or saddle points. The test relies on the behavior of the function's derivative in the vicinity of these critical points. Specifically, if the derivative changes sign at a critical point from positive to negative, the point corresponds to a local maximum. If the derivative changes sign from negative to positive, the point corresponds to a local minimum. If the derivative does not change sign at the critical point, it indicates a saddle point.

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