Global Maximum and Minimum

In this example problem, we are given a 3rd degree polynomial and an interval and asked to find the global (absolute) maximum (max) and global (absolute) minimum (min). To do so, we find the first derivative and factor it. We then determine the values of x that will make it equal to zero. These are referred to as critical values (numbers) and are the only values that our function could have local (relative) maximums or minimums. We then evaluate our original function at each of these critical values (numbers) AND at the endpoints of our given interval. We then compare the outputs and the largest is the global (absolute) maximum on that interval while the smallest is the global (absolute) minimum on that interval.
This video contains examples that are from Business Calculus, 1st ed, by Calaway, Hoffman, Lippman. from the Open Course Library, remixed from Dale Hoffman's Contemporary Calculus text. It was extended by David Lippman to add several additional topics. The text is licensed under the Creative Commons Attribution license. creativecommons.org/licenses/b...

[@sarthak1405]

Thank you sir

[@AGNIVO-kf2bl]

Thanks a lot professor

[@MathVideoTutorials]

My pleasure.

[@CementiHead]

thanks jit

[@MathVideoTutorials]

You're welcome.

[@enasgirave5773]

Thanks

[@MathVideoTutorials]

You are welcome. Glad it helped.

[@user-ph9xy6rz5h]

when you're solving these equations, please do it step by step because you didn't show how you arrived at the 3x^2-6x-9

[@YannickHollanda]

f(x)= original function f'(x)= derivative of function f''(x)= second derivative of function

[@MathVideoTutorials]

I didn't go into detail about the power rule for taking Derivatives. I've covered it in other videos so didn't elaborate in this one. Thanks for the feedback, I'll add more steps in my next videos.

[@similosihlegqalisisa8211]

👌👌👌

[@MathVideoTutorials]

Hope it helped.

[@similosihlegqalisisa8211]

@@MathVideoTutorials very much

[@lauragrabka538]

Thanks 🥹

[@MathVideoTutorials]

You’re welcome 😊