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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 22.

Calculus 1 / AB

Chapter 3

Applications of the Derivative

Section 2

The First Derivative Test

Derivatives

Missouri State University

Oregon State University

University of Michigan - Ann Arbor

Lectures

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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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Question 22. We found out that we have a minimum value at 02. And so using that as a critical value, we can plot it at zero to this is our minimum. It's gonna be too. And so we have increasing and decreasing on either side now do be careful because with exponents of fractions you're slopes will be different. Um and it won't be like an exact problem. It could be more like a V. Or like a very wide parabola. So that's something to keep in mind when you're plotting these, using only the critical points, but based on the information we found out from the first derivative, that is what we know.

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