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Problem

(a) Sketch the graph of a function that has a loc…

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Problem 10 Easy Difficulty

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

Absolute maximum at $ 2 $, absolute minimum at $ 5 $, $ 4 $ is a critical number but there is no local maximum and minimum there.


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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

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Derivatives

Differentiation

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Watch More Solved Questions in Chapter 4

Problem 1
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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
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Problem 45
Problem 46
Problem 47
Problem 48
Problem 49
Problem 50
Problem 51
Problem 52
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Problem 55
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Problem 61
Problem 62
Problem 63
Problem 64
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Problem 67
Problem 68
Problem 69
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Problem 80

Video Transcript

We're going to sketch the graph of function that is continuous and 15 And has an absolute maximum at to an absolute minimum at five and four is a critical number but there is no local maximum and minimum there. Okay, so the important thing this example is that for is a critical number but there is no local maximum and minimum there. And the thing is that if the function has a relative at that point for example and derivative must not exist because if if it exists then it means you should be zero, there is a judging lunch of your horizontal and in that case we will have a local maximum or minimum. So In order to there is no order that there is no local maximum and minimum there at four but it stills is a critical number. It means the narrative does not exist. For example, if the tunnel line is very good like in this example The change in line and four is a vertical line. So interpretive, it's not a number and uh evidently there is no Maximum nor minimum at four because around for there is to write and to the left there are images are that are bigger and smaller than the image at four. So it's not a law called nara minimum. So with that piece of that part and we can see that at five we have these uh lowest point in the whole graf and two we have the highest point in all the graph and in this case we have drawn and non differentiable A curve at the .2 but that's not a problem. Remember? The only request is the function is continuous on white five and he's the cases there is no discontinuities or jumps at any point and at two had the highest point on the graph of the function. He's also a local maximum, but is has requested the absolute maximum value. And at five we have here the absolute many men. and at four we don't have maximum or minimum and it's a critical point because the derivative does not exist at that point. So this is a solution to the given program.

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Related Topics

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Video Thumbnail

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Video Thumbnail

06:14

Review

A review is a form of evaluation, analysis, and judgment of a body of work, such as a book, movie, album, play, software application, video game, or scientific research. Reviews may be used to assess the value of a resource, or to provide a summary of the content of the resource, or to judge the importance of the resource.

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