Problem

Sketch the graph of a function $ f $ that is cont…

03:44

Question

Answered step-by-step

Problem 7 Easy Difficulty

Sketch the graph of a function $ f $ that is continuous on $ [1, 5] $ and has the given properties.

Absolute maximum at $ 5 $, absolute minimum at $ 2 $, local maximum at $ 3 $, local minima at $ 2 $ and $ 4 $

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

We are going to sketch the graph of a function that is continuous and 15. Close interval 1, 5 and has absolute maximum at five Absolute minimum at two. Local maximum at three. And local minimum at two and 4. And we have done that here. So we have this graph and as we can see and this graph we have a local minimum At two. This is the lowest point in the graph When we look close to the number two, but it's also the absolute minimum because if we look at the whole graph is the lowest point. So so what to we have local minimum and an absolute minimum. So we have those two parts. We have also local minimum at four as we as was stated here. Local minima at two and 4. So four. We have the local minimum because if you look close to the number four, the graph of the function has the lowest value at that point at the same happens around two but two, we also have the lowest point in the whole graf and that is the absolute minimum. Now we have a local maximum at three. And that's the case because at three we're at this point and if we look around that point, that is it. Um the higher his value when we look around Or nearly near the value three. So we have their local maximum but it's not a global maximum because the global maximum or the highest point in the graph when we look at the whole domain happens at this point here, which is five as expected Following the statement of sort of maximum five. And there is no There is neither a maximum or minimum at one. And it's important, the graph of this function is a continuous graph. That is we don't have any jumps or points to touch from the trend of the lines, only one piece, draw that his containers function. So we have this example this way of drawing a function with this property continues on 15 That's here to the meaningful and five close interval. And we have an absolute maximum at five here at this point, an absolute minimum at this point two. And we have a local maximum at three here and local minimum add to and four. So that's the that's one solution to the world. Yeah.

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