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If $ f'(x) = c $ ($ c $ a constant) for all $ x $, use Corollary 7 to show that $ f(x) = cx + d $ for some constant $ d $.

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Calculus 1 / AB

Calculus 2 / BC

Chapter 4

Applications of Differentiation

Section 2

The Mean Value Theorem

Derivatives

Differentiation

Volume

Missouri State University

Harvey Mudd College

Idaho State University

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.

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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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Okay, um we're being told that if f prime of X is equal to see and she is a constant for all X used Kerala very seven to show that f of X equals cfx. I mean, see explosive t with them constantly. So here, um in case you do not know what the Kerala very seven is and the Stuart textbook, I've restated it right here, and I'm going to stay there. So if f prime of X equals g prime back for all X and a B, then f of X equals G of X plus D for some constant d. So that is a statement. So we have to make a couple of assumptions. So we're told that F Prime of X is equal to see And in order to proceed with this, we're going to also create a function called G of X. So, So g of X, Um, we're gonna say it equals cfx so that when we take the derivative of G primary rex, it will equal See now, since primary, Rex and G Prime of X is equal to each other in this case, that and that's just a little case we made up. Um, we can actually apply Kerala very seven right away. Because corroborate 77 f prime lexical G prime of X. We can apply the statement f of X equals G of exports D So we can now. Now we can now use that formula f of X equals she of X Oh, dear. And since we have G FX, we can substitute that. You say after Becks is equal to see X plus d. Come on. And that is what we were asked. That's what we were being asked to prove so that of alphabetical cfx for the using corollary seven Oh!

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