Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

Locate all critical points.$$g(x)=\frac{x^{2}}{x^{2}-9}$$

$$(0,0)$$

Calculus 1 / AB

Chapter 3

Applications of the Derivative

Section 1

Extrema of a Function

Derivatives

Missouri State University

Baylor University

University of Michigan - Ann Arbor

University of Nottingham

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.

01:59

Locate all critical points…

02:28

Determine all critical poi…

02:31

01:01

02:09

01:47

01:55

Find all critical points o…

00:47

02:08

00:58

Find all critical numbers …

first we take the rabbit half to this function according to the formula of the derivative or cautions is to gravity of. Yes, the denominator is just the square of the previous denominator and the numerator equals the durability of other numerator times the denominator miners. The numerator times the derivative of the denominator. So the numerator is just miners 18 X. And we can factor the denominator into two parts Which X -3 and ex class than square recall that the critical number is a number of Amanda function in which a derivative is either zero or fields to exist. So a letter durability of equal zero or feels to exist. And hence When the derivative equals zero role acts because there and Gerardo fields to exist. X equals ray. On minor street the X equals zero. Its function value is also there. My X. Equals Rail -3. Its function value does not exist which means Soriana Manner three and not in the July of the function. And hence we only have one critical point. Trans arrow. There

View More Answers From This Book

Find Another Textbook

03:26

Consider $f(x)=4 x^{2 / 3},$ suppose you do not have a calculator and want t…

04:33

A kite maintains a constant altitude of 50 feet and is moving horizontally a…

01:53

Suppose that the manufacturer in Exercise 1 is forced to cut the selling pri…

03:33

Find $d y / d x$ at the indicated point in two different ways: (a) Solve for…

01:38

$f(x)=\left(x^{2}+3 x+1\right)^{17},$ find $f^{\prime}(x)$.

01:52

Find all the asymptotes and plot the graph of the given function.$$g(x)=…

01:05

The line $y=m x+b$ is called a slant or oblique linear asymptote of the func…

02:02

01:33

Determine the extrema of the function defined by the equation $f(x)=\frac{x}…

01:49

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