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Suppose $ f $ is differentiable on an interval $ l $ and $ f'(x) > 0 $ for all numbers $ x $ in $ l $ except for a single number $ c $. Prove that $ f $ is increasing on the entire interval $ l $.

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decreasing behavior

02:52

Wen Zheng

Calculus 1 / AB

Calculus 2 / BC

Chapter 4

Applications of Differentiation

Section 3

How Derivatives Affect the Shape of a Graph

Derivatives

Differentiation

Volume

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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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Suppose $f$ is differentia…

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Show that $f$ is different…

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okay. As we can see, the function is continuous. This is important because this means it doesn't change and the derivative is always equivalent to zero. We also know that the function grows because the first derivative is greater than zero. And we know that when the derivative is equivalent to zero, then approaches zero from the right hand side from a positive value. And then we know there's a point of infection where the graft changes con cavity. So the solution to this would be decreasing behavior and the given interval.

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