Find the absolute maximum and minimum of quadratic function on given interval

In this example problem, we find the absolute maximum (abs max) and absolute minimum (abs min) of a quadratic function (second 2nd degree polynomial) by taking its first 1st derivative and determining a critical value (critical number) by setting it equal to zero and solving for our variable. We then determine that the critical value will be a maximum of the function by using the second 2nd derivative test. Finally, we evaluate our critical number and the endpoints of the given interval in the original function. We compare the results to determine the absolute max and absolute min of the function and the values at which they occur.
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...

[@mitra.1]

is absolute maximum and strict global maximum same? can you please share some material to refer for strict global maxima

[@MathVideoTutorials]

Absolute maximum and global maximum are the same. This problem was on an interval but the process would be similar if there was not an interval.
If there was not an interval, focus on the leading term because the overall shape of the graph (and end behavior) will resemble that power function.
Odd degree: will not have an absolute/global maximum
Even degree:
Positive leading coefficient: will have absolute/global minimum at a critical value (critical number).
Negative leading coefficient: will have absolute/global maximum at a critical value (critical number).
After you find the critical values and know if you are going to have a max or min, evaluate all of the critical values in the original function. For a max, you are looking for the largest value. For a min, you are looking for the smallest.

[@whatskraken3886]

This guy sounds like huggbees

[@MathVideoTutorials]

Before this comment, I was not familiar with Huggbees but you are entirely correct.