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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 20.

Calculus 1 / AB

Chapter 3

Applications of the Derivative

Section 2

The First Derivative Test

Derivatives

Campbell 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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exercise 20 We had our critical points of zero negative seven as a minimum 1/4 and negative 809 9/1 28 as a maximum and negative one over negative and negative eight as a minimum. So to graph that we're going to have a very skewed graph just because I don't have enough through, we have let's plot our points of zero, negative seven, -1 -8 and 14 And -899 Over 1 28 We're worried about here. So what that would look like since we have a minimum here, a maximum in another minimum, you have a graph that looks something like this.

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