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Use the graph to state the absolute and local max…

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Problem 4 Easy Difficulty

For each of the numbers $ a $, $ b $, $ c $, $ d $, $ r $, and $ s $, state whether the function whose graph is shown has an absolute maximum or minimum, a local maximum or minimum, or neither a maximum nor a minimum.


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Wen Zheng

03:15

Carson Merrill

03:42

Gregory Higby

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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David Base G.

October 23, 2020

That was not easy, glad this was able to help

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Video Transcript

So in this problem we're given this graph and asked for each of the numbers A, B, c, D, r and S. State whether the function with this graph is an absolute maximum or minimum or local maximum or minimum, or neither of those. So let's start with a. So a is an end point out here. And as we can tell looking at the graph, it is not an absolute max as there are other parts of the graph above it that have higher values of Y. And it's not a minimum as there are other points below it as well. So it is neither a max nor a minimum. Okay, be so be as some kind of a minimum point but it looks like the point at our is actually lower than the point that be. So this is a local minimum. And especially since the curve is decreasing down to be going from left to right and then increasing past B. That makes it a local minimum as well. See by similar logic is going to be a local maximum in here as it is a maximum because the graph is increasing as we approach, see from the left and then decreasing as we go past, see heading on toward toward the right, okay, then, D Well, D is is a decreasing curve until we get to D and then it continues to decrease on past it. So D is neither a maximum nor a minimum and then our well, our is the lowest point we have of the curve. So our is both a local minimum. Right? As the graph is decreasing, going into our and then increases after our and it is our absolutely minimum for this function. Okay, So then the point S, as it's an endpoint, cannot be either a local men or local max, but it is the highest point on the curve, so s. Is an absolute maximum for this function, and so there we go.

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Related Topics

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Top Calculus 2 / BC Educators
Catherine Ross

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University of Michigan - Ann Arbor

Joseph Lentino

Boston College

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Lectures

Video Thumbnail

04:35

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.

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.

Join Course
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