Critical Points. Calculus-Applications of Derivatives: Optimization

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The critical points of a function are the points where the function changes direction. If the function was increasing and reaches a critical point, it starts decreasing there. Conversely, if a function was decreasing and reaches a critical point, then it starts increasing there. Therefore, the critical points of a function are the points that represent local maxima and minima of the function (its extrema). To find critical points, Take the derivative of the function and set the derivative equal to 0 Find the values of x that make the derivative equal to 0, or make it undefined. These are the critical numbers. Use the first derivative test to see whether or not the function actually changes direction at the critical numbers. Verify that the critical numbers are in the domain of the function.

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16 min 4 sec

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