I have been informed that on March 7th from 6:00am to 6:00pm Central Time Lamar University will be doing some maintenance to replace a faulty UPS component and to do this they will be completely powering down their data center.
Unfortunately, this means that the site will be down during this time. I apologize for any inconvenience this might cause.
Paul
February 18, 2026
Section 4.3 : Minimum and Maximum Values
2. Below is the graph of some function, \(f\left( x \right)\). Identify all of the relative extrema and absolute extrema of the function.
There really isn’t all that much to this problem. We know that absolute extrema are the highest/lowest point on the graph and that they may occur at the endpoints or in the interior of the graph. Relative extrema on the other hand, are “humps” or “bumps” in the graph where in the region around that point the “bump” is a maximum or minimum. Also recall that relative extrema only occur in the interior of the graph and not at the end points of the interval.
Also recall that relative extrema can also be absolute extrema.
So, we have the following absolute/relative extrema.
Absolute Maximum : \(\left( {6,8} \right)\)
Absolute Minimum : \(\left( {9, - 6} \right)\)
Relative Maximums : \(\left( {1,3} \right)\) and \(\left( {6,8} \right)\)
Relative Minimums : \(\left( { - 2, - 1} \right)\) and \(\left( {2, - 4} \right)\)