First Derivative Test

AP Calculus · Axiom Academy

Using sign changes to identify local max and min At a critical point, check whether the derivative changes sign. If it changes from positive to negative, you have a local max. If it changes from negative to positive, you have a local min. Test the sign of f'(x) on intervals between critical points Identify where the sign changes Conclusion: • At x = 0: f' changes from + to −, so local maximum • At x = 2: f' changes from − to +, so local minimum

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