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Sketch the graph of the function defined in the given exercise. Use all the information obtained from the first derivative.Exercise 21.

Calculus 1 / AB

Chapter 3

Applications of the Derivative

Section 2

The First Derivative Test

Derivatives

Campbell University

University of Michigan - Ann Arbor

University of Nottingham

Idaho State University

Lectures

04:40

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.

30:01

In mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value (the rate of change of the value of the function). If the derivative of a function at a chosen input value equals a constant value, the function is said to be a constant function. In this case the derivative itself is the constant of the function, and is called the constant of integration.

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Sketch the graph of the fu…

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Sketch the graphs of the g…

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No An exercise 21. We found that our maximum was at zero In two EN Route three. So let's plot that value right here and because it was a maximum you would have deep increasing on the left and decreasing on the right. Now, one thing we did find was at after zero, you didn't have any defined values, so that tells you something that the function does not go past Y equals zero. So when graphing this, if you do recognize the relationship in the function, you would have known that, or it would have been similar to that of a circle, so our graph will actually resemble a semicircle.

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