Problem

Sketch the graph of $ f $ by hand and use your sk…

02:33

Question

Answered step-by-step

Problem 17 Easy Difficulty

Sketch the graph of $ f $ by hand and use your sketch to find the absolute and local maximum and minimum values of $ f $. (Use the graphs and transformations of Section 1.2 and 1.3).

$ f(x) = 1/x $, $ x \geqslant 1 $

Video Answer

Solved by verified expert

Textbook Answer

Official textbook answer

Video by Oswaldo Jiménez

Numerade Educator

This textbook answer is only visible when subscribed! Please subscribe to view the answer

Watch More Solved Questions in Chapter 4

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

Problem 73

Problem 74

Problem 75

Problem 76

Problem 77

Problem 78

Problem 79

Problem 80

Video Transcript

here we are going to sketch the graph of the function F of x equal one over X. For X greater than or equal to one. And is that raft to find the absolute and local maximum and minimum values of the function. So here we have made a sketch of the graph. We know that if that one is one At two is 1 half, At three is 1/3 and so on. So the value of the function is decreasing or not. My anatomically and it never stopped decreasing. That is always increasing. It means the graph is always approaching the X axis or is getting closer to it as we go to the right but you never cross it. Or that is it never gets a value that is on the X axis. But it's always approaching or getting closer to. That means that limit when X grows without any bound. That is what eggs goes to plus infinity is zero. But coming from positive values, that is the function is always positive. That's the behavior of dysfunction. And we can see clearly that the highest point in the graph in this case, that is included in the graph is F of one which is equal to one. So if of one equal one is the absolute maximum value of the function. That is because we have considered function only for X rather than or equal to one for A Square. That articles one. And that is the sort of maximum values one and is obtained in fact at X Equal one. So we have this result, we have no local maximum for this function remember we can consider this same value as local maximum because we have we don't have any graph to the left of the functions. So we only consider local streams inside of the main the endpoints of the interval. So in this case there is no local maximum, right? And there is no absolute minimum either has no absolute minimum or local minimum and that's because there is no lowest point in the graph, that is the graph is all with descending. It's never never stopped descending, so there is no longer with wine. The thing is that it is descendant but in a way that it will never touch the exact size of the descending, never stopped. And for that reason there is not the lowest point in the graph. And so there is no absolute medium and for similar situation there is no local minimum, so we don't have either of those. And in summary the function has only an absolute maximum value of one Attain or the course at execute one. And that the characteristics off or the properties of the function F Mexico one over X for X prison records one

Get More Help with this Textbook

James Stewart

Calculus: Early Transcendentals

View More Answers From This Book

Find Another Textbook

Study Groups

Study with other students and unlock Numerade solutions for free.

Problem