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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 23.

Calculus 1 / AB

Chapter 3

Applications of the Derivative

Section 2

The First Derivative Test

Derivatives

Baylor University

Idaho State University

Boston College

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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The information we got from exercise 23, we know that we have Three critical points. So to graph it, we have 05 as our maximum. We must make three right there and then we have one three and -13 as our minimums. So if we were to graph it would look something like this and keep in mind this is a very rough graph. Just because we don't know the exact shape or the slopes faced. I mean we do, but it's not going to be completely accurate based on the critical points that we derived from the different derivative, but this is the general shape.

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