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Locate all critical points.$$r(x)=4 x^{3 / 4}+2$$

$$(0,2)$$

Calculus 1 / AB

Chapter 3

Applications of the Derivative

Section 1

Extrema of a Function

Derivatives

Harvey Mudd College

University of Michigan - Ann Arbor

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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Classify all critical poin…

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Locate all critical points…

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Find all critical points x…

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Find all the critical poin…

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Determine all critical poi…

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Find all critical points o…

First, let's reveal the definition of critical points. Any numbering of Jeremiah function at which the derivative zero field to exist. It's called a critical number. If C is a critical number for the function, then the part C f C is called a critical point. So first we take the derivative to this function. It's directed areas our prime X echoes. Free time acts to the power of minors one force, and we can rewrite it as three over X to a power of one force. I know that it's the relative cannot be zero. It accounts only feels to exist, which means it's value is infinite and hence gets a critical number which is X equals zero. And the functional value at his steroid is too, and hence it has one critical point which is 02

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