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

Determine the equation of the tangent line to the given curve at the indicated $x$ -value.$$f(x)=\frac{x^{2}+3}{x^{2}-3}, \quad x=1$$

$y=-3 x+1$

Calculus 1 / AB

Chapter 2

An Introduction to Calculus

Section 5

Derivative Rules 2

Derivatives

Missouri State University

Campbell University

Harvey Mudd College

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.

02:26

Determine the equation of …

05:24

01:53

Find the equation of the t…

02:37

04:22

Find an equation of the ta…

were asked to find the tangent line. And any time you need the change of line, you better have the point and slope eso. It's nice about this problems. They give you the export. Well, I guess they have to give you the X coordinate. And what they also need to find is the derivative. When Nexus One was that would tell me the slope. So as we look at the problem, we have X squared plus three over X squared minus three. So the first thing is to plug in one into that all of those excess. And so what? We end up with this four and plugging one in for this X as well, uh, you get one minus three, which would be negative too. So you get a wide coordinate of negative two in the problem. But now what you need is the derivative of that, and that's using the question. So the question roses take the drift of the top. Leave the bottom alone, Uh, minus. Take the derivative of the bottom, leave the top alone all over the denominator square. Now, the way I would do this problem is not simplify this because we've already plugged in one. And for all these export plus threes, which were four, um, X is one excess one. This was negative. Two So and the denominator is also negative. Two squared so real quick. I already know that negative to square this 42 times negative too. And give me negative for and then two times forward. Give me eight eso. I'm looking at negative 12 force, which would equal negative three. So now what I can do is I can come up with the equation using point slope form. Why equals a slope X minus the X coordinate, plus the y coordinate. And I would leave my answer like that. Otherwise you could distribute this in and you'll get negative. Three X plus three minus two would be plus one would be another acceptable answer. So this slope intercept form

View More Answers From This Book

Find Another Textbook

02:07

Consider Figure $13,$ which shows the intersection of two lines. Determine t…

06:36

Given the two parallel lines $y=m x+b$ and $y=m x+B,$ determine the perpendi…

03:02

If $y^{3}=2 x^{2},$ determine $d x / d t$ when $x=2$ and $d y / d t=4$.

02:44

Show if $a b \neq 0,$ then the line with intercepts $(a, 0)$ and $(0, b)$ ha…

05:35

Determine the equation of the tangent line to the given curve at the indicat…

01:11

$f(x)=x^{4},$ find $f^{\prime}(x), f^{\prime \prime}(x), f^{(3)}(x)$ and $f^…

01:13

Find the average rate of change of $y$ with respect to $x$ on the given inte…

04:48

Plot each of the following lines on the same set of axes. (a) $y=2 x$(b)…

03:09

180,000 square feet of land is to be enclosed in a rectangular plot which wi…

05:19

(a) A farmer has a field bordering a straight river. He wants to design a re…