Refer a friend and earn $50 when they subscribe to an annual planRefer Now

Get the answer to your homework problem.

Try Numerade Free for 30 Days

Like

Report

Find an equation of the tangent line to the curve at the given point.

$ y = \ln (x^2 - 3x + 1), (3, 0) $

$y-0=3(x-3)$

00:51

Frank L.

02:27

Madi S.

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 6

Derivatives of Logarithmic Functions

Derivatives

Differentiation

Harvey Mudd College

Baylor University

University of Michigan - Ann Arbor

Lectures

03:09

In mathematics, precalculu…

31:55

In mathematics, a function…

0:00

Find an equation of the ta…

02:00

01:59

01:15

02:53

Find an equation for the t…

07:57

Find the equation of the t…

04:20

01:28

01:02

02:37

and this problem. We're finding the equation for the tangent line to a curve. Specifically, the function of that curve is log rhythmic, and we're also given a point at which we have to find the tangent line. So the function were given is why equals the natural log of X squared minus three x plus one. So the first thing that we need to do before we can find the tangent line is find the derivative. So we need Y prime. How are we going to do that? We have to use training role. So why prime would be equal to one over X squared minus three x plus one times two X minus three. Now, if you're confused about that, basically what you do with chain rule because we know the derivative of the natural log is one over X, so we would have one over X. But in this case, it's this entire input and then we'll multiply by the derivative of that input. And then we can simplify Why? Prime to be two X minus three over X squared minus three X plus one. So we have the derivatives, but we need the slope of the tangent mind at the 0.30 so we can find why, prime of three, why crime of three would be equal to sticks minus 3/9 minus nine plus one so it would simplify to three. And now we're very close to finding the equation for a tangent line. We can use this point slope form why, minus why not equals m times X minus x dot So we can just plug in the point that were given why my zero equals three times X minus three. So you can essentially write the tangent line in this form or you can simplify it in point in slope form and we would have Why equals to reacts minus nine. So either way, they both mean the same thing. These air both the equation for the tangent line to our curve at that point. So I hope that this problem helped you understand a little bit more about how we confined the equation for a tangent line, using our knowledge of differentiation of logarithmic functions and then plugging in the point in our, um, coordinate plain to find the overall tangent line

View More Answers From This Book

Find Another Textbook

Numerade Educator

In mathematics, precalculus is the study of functions (as opposed to calculu…

In mathematics, a function (or map) f from a set X to a set Y is a rule whic…

Find an equation of the tangent line to the curve at the given point.$ y…

Find an equation for the tangent line to the graph at the specified value of…

Find the equation of the tangent line at the given point on each curve.$…

Find the equation of the tangent line at the given point on each curve. …

Find the equation of the tangent to the graph of $y=3 x^{2}-x$ at $x=1$

Find an equation of the tangent line to$$f(x)=2 \ln x^{3}$$

Find an equation of the tangent line at the given point. If you have a CAS t…

00:40

Find the derivative of the function. Simplify where possible.$ R(t) = \a…

01:33

(a) Suppose $ f $ is a one-to-one differentiable function and its inverse fu…

01:26

Use the form of the definition of the integral given in Theorem 4 to evaluat…

01:04

If $ A $ is the area under the curve $ y = e^x $ from 1 to 3, use Exercise 2…

03:18

Find $ \frac {d^9}{dx^9}(x^8 \ln x). $

01:22

Use the graphs of $ f $ and $ g $ and their tangent lines at $ (2, 0) $ to f…

00:27

In Example 6 we considered a bacteria population that doubles every hour. Su…

00:38

Express the limit as a definite integral on the given interval.

$ \d…

00:28

The velocity graph of a car accelerating from rest to a speed of 120 km/h ov…

01:55

(a) Find the intervals of increase or decrease.(b) Find the local maximu…

92% of Numerade students report better grades.

Try Numerade Free for 30 Days. You can cancel at any time.

Annual

0.00/mo 0.00/mo

Billed annually at 0.00/yr after free trial

Monthly

0.00/mo

Billed monthly at 0.00/mo after free trial

Earn better grades with our study tools:

Textbooks

Video lessons matched directly to the problems in your textbooks.

Ask a Question

Can't find a question? Ask our 30,000+ educators for help.

Courses

Watch full-length courses, covering key principles and concepts.

AI Tutor

Receive weekly guidance from the world’s first A.I. Tutor, Ace.

30 day free trial, then pay 0.00/month

30 day free trial, then pay 0.00/year

You can cancel anytime

OR PAY WITH

Your subscription has started!

The number 2 is also the smallest & first prime number (since every other even number is divisible by two).

If you write pi (to the first two decimal places of 3.14) backwards, in big, block letters it actually reads "PIE".

Receive weekly guidance from the world's first A.I. Tutor, Ace.

Mount Everest weighs an estimated 357 trillion pounds

Snapshot a problem with the Numerade app, and we'll give you the video solution.

A cheetah can run up to 76 miles per hour, and can go from 0 to 60 miles per hour in less than three seconds.

Back in a jiffy? You'd better be fast! A "jiffy" is an actual length of time, equal to about 1/100th of a second.