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Use the graph to state the absolute and local maximum and minimum values of the function.

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01:27

Wen Zheng

Calculus 1 / AB

Calculus 2 / BC

Chapter 4

Applications of Differentiation

Section 1

Maximum and Minimum Values

Derivatives

Differentiation

Volume

Oregon State University

Harvey Mudd College

University of Nottingham

Boston College

Lectures

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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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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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Use the graph to state the…

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Find all local maximum and…

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Find the absolute maximum …

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So what? We see if we look at the graph, um, it won't be perfect, but it's okay. What we have here is value. It comes down to value about here. Then this comes up and goes down, and then this comes up again and goes right here. So what we see is that the absolute minimum value is clearly going to occur when X equals four. And that's this. How you're right here. So it's the absolute minimum, um, and that that would also be considered a local minimum. Then we have a local maximum occurring at three. That's right here. We also have a local maximum occurring at six. So that's this point right here. Then. Lastly, we have our local minima, which already said, there's one right here at X equals four, but then we also have one. Um, since there's a point right here, this is considered a local minima at X equals two because we see that every point to the right is increasing. Every point to the left is increasing immediately thereafter.

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