FIRST DERIVATIVE TEST to find the max and min (KristaKingMath)

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The first derivative test is the tool you use to test the potential critical points of a function to see whether or not they are actually critical points. You can use the first derivative test to describe the behavior of the function on either side of the critical point. Or, to put it another way, you can use the first derivative test to say whether the function is increasing or decreasing on either side of the critical point.

If you can use the first derivative test to show that the function is increasing on one side of the critical point and decreasing on the other, then by the first derivative test you've proven that the potential critical point is an actual critical point, and therefore that the function has at least a local maximum or local minimum there, if not a global maximum or global minimum.

In order to use the first derivative test, pick values on either side of the critical point, and plug them into the first derivative of the function. If the result is positive, then the function is increasing on that side of the critical point. On the other hand, if the result is negative, then the function is decreasing on that side of the critical point.

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