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Classify all critical points.$f(x)=4 x^{5}$

$$\mathrm{N}(0,0)$$

Calculus 1 / AB

Chapter 3

Applications of the Derivative

Section 2

The First Derivative Test

Derivatives

Oregon State University

University of Michigan - Ann Arbor

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.

00:50

Locate all critical points…

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Classify all critical poin…

02:16

Determine all critical poi…

03:53

02:55

01:08

Find the critical points o…

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Find all the critical poin…

02:37

Find and classify the crit…

01:53

So we have Or into the 5th. We want to find the derivative of this. First to find out before we look at any critical points. So we have 20 x to the fourth. Using power rule as our derivative. Now we are going to find out where this equals zero by solving it, you find out that X equals zero, you're derivative zero. So we know that this is the location of a critical point. That is to determine what kind. We're going to pick values slightly above and slightly below. We have negative one and positive one. And we're gonna look at what That makes the derivative function. So we know at zero hour derivative function equals zero. Now at negative one, if you were to plug it into here, you get a positive value and at one you also get a positive value since you have something being Race of 4th Power. So you know that you're derivative is increasing, then it's at zero and then it's increasing again, which means you have a point of inflection. So it's 00. You have and or in a point of inflection

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