 Let's take a look at an example of how to locate absolute extrema of a function. Remember that absolute extrema are going to occur either at the critical numbers of the function or at the end points of the closed interval. Remember also that critical numbers of a function are found where the derivative equals zero or the derivative does not exist. So let's go ahead and find the derivative of this and and we'll set it equal to zero because it is a polynomial function. There is no place that the derivative will be undefined, so we don't have to worry about that. We'll go ahead and solve this out by factoring out a greatest common factor and we find that our critical numbers, we have two of them, x equals zero and x equals one. These are our critical numbers. So absolute extrema are going to occur either at these critical numbers or at the end points of the function. So we need to evaluate all four of these values, the two critical numbers, and the two end points of the interval into the function. So we'll have to do f of negative one, f of two. It does not matter the order in which you do this and finally f of one. This part you can simply do on your calculator by substituting in. Give it a try and hopefully you get the same things I do and hopefully they're the y values. It's the y value that's going to dictate which is your absolute maximum versus your absolute minimum. Obviously 16 is the highest y value, so that tells us we have an absolute maximum and I'm just going to use the ordered pair of the point 2 comma 16. The lowest of all these of the y values, negative one, that dictates where our absolute minimum then is. And since it's a different point, I'll use the letter q. Now depending upon the directions, they might have asked you what the absolute extrema value is. Remember if that's the way in which the directions were worded, the once specifically the y value only, as your answer. Or they might have asked you where the absolute extrema occur. That typically implies either the ordered pair, such as we gave it here, or simply just the x value.