How to Find Local Maximum and Minimum Values of a Polynomial Function | Glass of Numbers

In this video, we use the First Derivative Test to find the local maximum and minimum values of a polynomial function.

How to find the local extreme values? We first need to find critical numbers of the function. Then plot the critical numbers on the number line (x-axis) to construct a sign analysis chart. This chart will tell us on what interval the function is increasing or decreasing. We can next apply the First Derivative Test to find the local maximum and minimum values.

Note that because we are finding the max and min values, we will finding the y-values of the function. Do not confuse this with the location of the extrema, which are the x-values.

See here how to find local extreme values for a rational function:
youtu.be/dw_ujbbN8ys

See here how to deal with a trigonometric function with infinitely many local max and min:
youtu.be/ONoe__gaC0g

See here how to find the local extreme values for a sum of exponential function:
youtu.be/pWmkjcSb5J8

See here how to find the local extreme values for a polynomial function in factored form:
youtu.be/jRQBWa6sQgg

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