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Find the absolute maximum and minimum values of each function on the given interval. Then graph the function. Identify the points on the graph where the absolute extrema occur, and include their coordinates.$$f(x)=x^{2}-1, \quad-1 \leq x \leq 2$$

Absolute maximum: 3 absolute minimum: -1

Calculus 1 / AB

Chapter 4

Applications of Derivatives

Section 1

Extreme Values of Functions on Closed Intervals

Derivatives

Differentiation

Applications of the Derivative

Missouri State University

Campbell University

Harvey Mudd College

University of Michigan - Ann Arbor

Lectures

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this question were given the function after vax Eagle two X squared minus one onto interval from night of one is not able to x, which is lost people to to when were asked to find the absolute extreme bodies which is our absolute maximum in are absolutely love. So start off with when I find any critical number is so we know that this is a derivative of your backs off prime of X is equal to using. All right, let's see, We can take our two new friends and we drop our drop Our power to get us to X and two X is equal to zero an exit ticket 07 state critical numbers are X equals zero. So when we're finding our absolute maximum minimums organised our side links and then our people about loose. So we have s of negative one which is equal to maybe one squared minus one which is just equal to zero. It's up from zero which is equal to zero squared. My swan, which is equal to native one we have to, which is equal to two squared minus 12 is equal to three and so we can see that are absolute minimum is, uh, to negative one, their absolute acts. Mom, is that three? Now? The next thing we should do is we need to cross this so we can go to does my Swede X squared minus one on the interval from We have nice one. His last three equal to X, which is Lester unequal to to And so we can see that we have our absolute minimum at zero negative one and in an absolute maximum that 23 So we so this will be our answer.

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