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Sketch the graph of a function that satisfies all of the given conditions
Vertical asymptote $ x = 0 $, $ f'(x) > 0 $ if $ x < -2 $,$ f'(x) < 0 $ if $ x > -2 (x \not= 0) $,$ f"(x) < 0 $ if $ x < 0 $, $ f"(x) > 0 $ if $ x > 0 $
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03:01
Fahad Paryani
Calculus 1 / AB
Calculus 2 / BC
Chapter 4
Applications of Differentiation
Section 3
How Derivatives Affect the Shape of a Graph
Derivatives
Differentiation
Volume
Missouri State University
Baylor University
University of Michigan - Ann Arbor
University of Nottingham
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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Sketch the graph of a func…
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Sketch a graph of a functi…
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Sketch the graph of the fu…
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Okay, so we're given four conditions that are graph has to meet you have this vertical ascent owed at X is equal to zero. We are increasing or are derivative is greater than zero when X is less than negative two were decreasing when X is greater than negative two. And our second derivative is less than zero for X being less than zero. And our second derivative being less than zero means that we are just concave down on the interval from negative infinity to zero. And so what I've drawn already is just the vertical ascent to X is equal to zero. And I put on the X axis this point negative too. Since that's the point where we go from increasing to decreasing. So I'm just gonna put a point up here as the point that we go from increasing to decreasing, which means that it is a local maximum. Or it could be an absolute maximum as well, but we're guaranteed to have a maximum at this point since we're going from increasing and decreasing. And so I'm going to draw a line that is concave down and increasing up until this point here just call that the point and now we're decreasing. Still concave down and we have this vertical ascent tote so we're never going to go past X is equal to zero. And now what we can do is we can actually just stop there since we don't have any conditions for X being greater than zero. So the important thing to remember is that we're decreasing until X is equal to negative two. And then we are sorry, we're increasing until X is equal to negative two. And then we start decreasing. And since we have this vertical ascent, oh, we're never going to go past zero. And we have to be always concave down which we are Yeah.
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