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Find the critical numbers of the function.

$ f(x) = x^3 + 6x^2 - 15x $

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Madi Sousa

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Oswaldo Jiménez

Calculus 1 / AB

Calculus 2 / BC

Chapter 4

Applications of Differentiation

Section 1

Maximum and Minimum Values

Derivatives

Differentiation

Volume

Bella F.

October 29, 2020

this was kinda funny

Jake N.

March 6, 2019

Nice video mate. Great Job

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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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Find the critical numbers …

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Okay. So our goal is to find the critical points. So we're going to find critical points. And as a reminder critical points. Our winner derivative Equal zero or DNE though in this case we only have the zero case. So let's go ahead and find our derivative. We'll use power role. So F prime of X is three X squared Plus 12. Acts -15 by power role. And we want to set this equal to zero but I'm going to go ahead and um factor at first I can pull out um a common three just to clean it up a little bit. So what what's left in the parentheses? That is X squared plus four X minus five. That does help me to see that. I can factor that as X-plus five and X minus one. We saw the three in front but we're going to set that equal to zero. Um It's not a D N. A case. It's just a zero case. So therefore either X plus five equals zero or X -1 equals zero. So therefore x equals -5 or X equals one. Um So those are critical points. So the critical points. Um and we're gonna go ahead. Let's go ahead. Um And find the well actually we only need critical numbers so we didn't need the Y. Value. So let's just go down here are critical numbers Are x equals -5 and X equals one. If we wanted the critical points meaning the Y value. Also we would just plug in each of the X value into the original ffx, get our Y value and then we'd have the actual point. In terms of critical numbers, we have done it alright, Have a wonderful day.

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