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Problem

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

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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 $


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Fahad Paryani

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Chris Trentman

Related Courses

Calculus 1 / AB

Calculus 2 / BC

Calculus: Early Transcendentals

Chapter 4

Applications of Differentiation

Section 1

Maximum and Minimum Values

Related Topics

Derivatives

Differentiation

Volume

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Top Calculus 2 / BC Educators
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Volume - Intro

In mathematics, the volume of a solid object is the amount of three-dimensional space enclosed by the boundaries of the object. The volume of a solid of revolution (such as a sphere or cylinder) is calculated by multiplying the area of the base by the height of the solid.

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06:14

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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.

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Related Topics

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Grace He

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Review

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