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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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02:12

Wen Zheng

03:15

Carson Merrill

03:42

Gregory Higby

Calculus 1 / AB

Calculus 2 / BC

Chapter 4

Applications of Differentiation

Section 1

Maximum and Minimum Values

Derivatives

Differentiation

Volume

David Base G.

October 23, 2020

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Campbell University

University of Michigan - Ann Arbor

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For each of the numbers $ …

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For each of the numbers $a…

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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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