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Locate all critical points.$$f(x)=\frac{x+3}{x-3}$$

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Calculus 1 / AB

Chapter 3

Applications of the Derivative

Section 1

Extrema of a Function

Derivatives

Missouri State University

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University of Michigan - Ann Arbor

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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Locate all critical points…

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Determine all critical poi…

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Find all the critical poin…

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Find all critical points o…

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Classify all critical poin…

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Find and classify the crit…

first let's reveal the definition of critical points. Any number of the demise of a function at which the derivative is either zero or feels to exist. It's called a critical number. If say is a critical number for the function, then c f C is called a critical point. So first let's take the relatives to this function according to the formula of the derivative of cautions have prime acts vehicles. The denominator is just the square of the previous denominator which is at minus three square and the numerator is a derivative of the numerator, which is one times the general nature miners. The derivative of the denominator, which is one miners, the numerator and we can rewrite this. S the denominators do x minus three squared and the numerator is minus six. Know that the derivative cannot be zero and has, it can only feels to exist and its value is infinite and hence we know that acts because it's great. But when article three, the functional value is meaningless. That is X equals raise not in the domain of the function and enhance. This function has no critical point.

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Classify all critical points.$f(x)=x^{2}-2 x+3$