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Find the critical numbers of the function.

$ f(x) = 4 + \frac{1}{3}x - \frac{1}{2}x^2 $

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01:01

Fahad Paryani

01:15

Chris Trentman

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

Baylor University

University of Michigan - Ann Arbor

Lectures

04:35

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.

06:14

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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Find all critical numbers …

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who would like to find? The critical numbers of the function F. Of X equal four plus one third X minus one half X square. Not that the critical numbers of the function. Our numbers into the main of these functions such that Mhm. Such that the derivative at that point doesn't exist or is zero. So that's it. That's his finishing. And first of all, the domain of the given function is the real numbers. I'm talking now about this function. That is because it is it's a polynomial of second degree. So is well defined at every real number eggs. And so the domain of the function of the whole real numbers. Mhm. Now let's see what is the derivative of F at any point is one third minus X. Because his negative 1/2 times two Times X. to the one. So this is a derivative is defined at every point in the real numbers. So the derivative exists for any real number. That is for any X. In the domain of the function. So this part do not apply in this case, So we only get five points for the theory of a TV- zero. Yeah. So the derivative of this function is zero if and only if one third minus six is zero, which is equivalent to X Equal 1 3rd, and that's the only value for which the derivative zero. And taking into account that it exists everywhere, it is well defined and exists at every real number. I'm talking about the relative, then this is the only critical point to conduct critical number of fx equal four plus one third of x minus one half X. Square. Yes, X Equal 1 3rd. Mhm. So this is you find out the answer.

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