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

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

See here how to deal with a trigonometric function with infinitely many local max and min:

See here how to find the local extreme values for a sum of exponential function:

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#Calculus #LocalExtrema #CurveSketching

[erikamoreno]

Why did you leave out the 3x and the 2x why didn’t you distribute that part

[zaeemahmad]

Great video! I wanted to know what app/software you are using to write this math. Looks really good. Thanks in advance.

[elyk]

Did you change the sign of the 2 2s on the critical numbers?

[nomiwrites]

Plz tell if the denominator is 0...by putting any of value....for is in denominator...then at -2 function is undefined ....so please explain that case...

[tef]

Great video thanks a lot! What happens if the numerator is -2(x^2 -2x+4)? Does that mean there aren't any critical numbers for that function? There doesnt seem to be any explanation on that anywhere

[miavuong]

thank you so much, this was a very helpful video!!

[artemis]

Thank you so much sir for this awesome video 👍👍👍

[daylatharraulima]

so the f' DNE is going to be the singular point, am i right?