Enroll in one of our FREE online STEM summer camps. Space is limited so join now!View Summer Courses

Georgia Southern University

Problem 1
Problem 2
Problem 3
Problem 4
Problem 5
Problem 6
Problem 7
Problem 8
Problem 9
Problem 10
Problem 11
Problem 12
Problem 13
Problem 14
Problem 15
Problem 16
Problem 17
Problem 18
Problem 19
Problem 20
Problem 21
Problem 22
Problem 23
Problem 24
Problem 25
Problem 26
Problem 27
Problem 28
Problem 29
Problem 30
Problem 31
Problem 32
Problem 33
Problem 34
Problem 35
Problem 36
Problem 37
Problem 38
Problem 39
Problem 40
Problem 41
Problem 42
Problem 43
Problem 44
Problem 45
Problem 46
Problem 47
Problem 48
Problem 49
Problem 50
Problem 51
Problem 52
Problem 53
Problem 54
Problem 55
Problem 56
Problem 57
Problem 58
Problem 59
Problem 60
Problem 61
Problem 62
Problem 63
Problem 64
Problem 65
Problem 66
Problem 67
Problem 68
Problem 69
Problem 70
Problem 71
Problem 72

Need more help? Fill out this quick form to get professional live tutoring.

Get live tutoring
Problem 50

a. Identify the function's local extreme values in the given domain, and say where they occur.

b. Which of the extreme values, if any, are absolute?

c. Support your findings with a graphing calculator or computer grapher.

$$

f(x)=\sqrt{x^{2}-2 x-3}, \quad 3 \leq x<\infty

$$

Answer

tee the graph

You must be logged in to like a video.

You must be logged in to bookmark a video.

## Discussion

## Video Transcript

So here we have affects is he square it of X squared minus two X minus three on the domain X between three and infinity. Let's go and take the derivative To find the critical points that's gonna be one over to square it X squared minus two X minus three and then apply the chain rule. So on top will have two X minus two. And so when does f prime Nickel zero plus, when the numerator is euros, seven x is one, but notice that X is one is not into domain. So we'LL throw that one away And when his f prime undefined Well, that's gonna happen when the denominators zero. So, in other words, when x squared minus two x prentiss three zero. Okay, if you factor this this is X minus three times X plus one call zero. So you have excess three or exits, negative one. It can notice. The negative one is not the domain. It's our only critical point is a three killer. So then we only all we need to know is whether or not this function is increasing or decreasing after three well free plug in, say, four. We're going to get eight minus twos. That's positive. F crime is going to be positive, so this function is increasing after three. So that means we have a local minimum. So again, this is going to be positive honor to me. So we have a local men whenever the function starts at X equals three, three of and the value is f of three, which is here, and this will also be an absolute mess because it's going to increase after. For ex greater than three, it's going to increase off to infinity, so there's no absolute maximum.

## Recommended Questions