Download the App!

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

Sent to:
Search glass icon
  • Login
  • Textbooks
  • Ask our Educators
  • Study Tools
    Study Groups Bootcamps Quizzes AI Tutor iOS Student App Android Student App StudyParty
  • For Educators
    Become an educator Educator app for iPad Our educators
  • For Schools

Problem

If $ f(2) = 10 $ and $ f'(x) = x^2 f(x) $ for all…

01:13

Question

Answered step-by-step

Problem 47 Medium Difficulty

If $ g(x) = xf(x), $ where $ f(3) = 4 $ and $ f'(3) = - 2. $ find an equation of the tangent line to the graph of $ g $ at the point where $ x = 3. $


Video Answer

Solved by verified expert

preview
Numerade Logo

This problem has been solved!

Try Numerade free for 7 days

Clarissa Noh
Numerade Educator

Like

Report

Textbook Answer

Official textbook answer

Video by Clarissa Noh

Numerade Educator

This textbook answer is only visible when subscribed! Please subscribe to view the answer

More Answers

00:57

Frank Lin

Related Courses

Calculus 1 / AB

Calculus: Early Transcendentals

Chapter 3

Differentiation Rules

Section 2

The Product and Quotient Rules

Related Topics

Derivatives

Differentiation

Discussion

You must be signed in to discuss.
Top Calculus 1 / AB Educators
Anna Marie Vagnozzi

Campbell University

Samuel Hannah

University of Nottingham

Michael Jacobsen

Idaho State University

Joseph Lentino

Boston College

Calculus 1 / AB Courses

Lectures

Video Thumbnail

04:40

Derivatives - Intro

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.

Video Thumbnail

44:57

Differentiation Rules - Overview

In mathematics, a differentiation rule is a rule for computing the derivative of a function in one variable. Many differentiation rules can be expressed as a product rule.

Join Course
Recommended Videos

03:46

If $g ( x ) = x f ( x ) ,$…

04:39

If $g(x)=x f(x)$, where $f…

03:13

The line tangent to the gr…

01:43

g(x) is the tangent line t…

02:44

Find the equation of the l…

01:36

Find the slope of the tang…

01:30

Find an equation of the ta…

01:44

Given that $f(-2)=3$ and $…

01:03

Suppose $f(3)=1$ and $f^{\…

03:43

Find an equation of the ta…

02:05

Find the equation of the t…

01:56

Find $f^{\prime}(x)$ and t…

Watch More Solved Questions in Chapter 3

Problem 1
Problem 2
Problem 3
Problem 4
Problem 5
Problem 6
Problem 7
Problem 8
Problem 9
Problem 10
Problem 11
Problem 12
Problem 13
Problem 14
Problem 15
Problem 16
Problem 17
Problem 18
Problem 19
Problem 20
Problem 21
Problem 22
Problem 23
Problem 24
Problem 25
Problem 26
Problem 27
Problem 28
Problem 29
Problem 30
Problem 31
Problem 32
Problem 33
Problem 34
Problem 35
Problem 36
Problem 37
Problem 38
Problem 39
Problem 40
Problem 41
Problem 42
Problem 43
Problem 44
Problem 45
Problem 46
Problem 47
Problem 48
Problem 49
Problem 50
Problem 51
Problem 52
Problem 53
Problem 54
Problem 55
Problem 56
Problem 57
Problem 58
Problem 59
Problem 60
Problem 61
Problem 62
Problem 63
Problem 64

Video Transcript

Hey, it's clear. So when you read here, so our first gonna use the product roll to find the derivative of G. So it g of X is equal to x times athletics. So the derivative of G it's gonna be equal to that of acts plus x times the derivative of Then we're gonna find too derivative after we plug in three Fergie, the derivative of G of three. And we're gonna use our given values three times the derivative of us of three, which is equal to four plus three times negative too, which is equal to negative, too. So this is gonna be the Slope M of detention line to G of X at X equals three. And we need to find the value for G up three. And we get well, so our line equation why minus y one equals M on X minus X one, and all we do is just plug in, make it why is equal to negative two x plus 18

Get More Help with this Textbook
James Stewart

Calculus: Early Transcendentals

View More Answers From This Book

Find Another Textbook

Study Groups
Study with other students and unlock Numerade solutions for free.
Math (Geometry, Algebra I and II) with Nancy
Arrow icon
Participants icon
192
Hosted by: Ay?Enur Çal???R
Math (Algebra 2 & AP Calculus AB) with Yovanny
Arrow icon
Participants icon
82
Hosted by: Alonso M
See More

Related Topics

Derivatives

Differentiation

Top Calculus 1 / AB Educators
Anna Marie Vagnozzi

Campbell University

Samuel Hannah

University of Nottingham

Michael Jacobsen

Idaho State University

Joseph Lentino

Boston College

Calculus 1 / AB Courses

Lectures

Video Thumbnail

04:40

Derivatives - Intro

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.

Video Thumbnail

44:57

Differentiation Rules - Overview

In mathematics, a differentiation rule is a rule for computing the derivative of a function in one variable. Many differentiation rules can be expressed as a product rule.

Join Course
Recommended Videos

03:46

If $g ( x ) = x f ( x ) ,$ where $f ( 3 ) = 4$ and $f ^ { \prime } ( 3 ) = - 2 …

04:39

If $g(x)=x f(x)$, where $f(3)=4$ and $f^{\prime}(3)=-2$, find an equation of th…

03:13

The line tangent to the graph of $f$ at $x=3$ is $y=4 x-2$ and the line tangent…

01:43

g(x) is the tangent line to the graph of $f(x)$ at $x=a$. Graph $f(x)$ and $g(x…

02:44

Find the equation of the line tangent to $f(x)$ at $x=2$, if $$f(x)=\frac{x^{3}…

01:36

Find the slope of the tangent line to the graph of the function at the given po…

01:30

Find an equation of the tangent line to the graph of $y=f^{\prime}(x)$ at $x=3$…

01:44

Given that $f(-2)=3$ and $f^{\prime}(-2)=-4,$ find an equation for the tangent …

01:03

Suppose $f(3)=1$ and $f^{\prime}(3)=4 .$ Let $g(x)=x^{2}+f(x)$ and $h(x)=3 f(x)…

03:43

Find an equation of the tangent line to the graph of $y=f(x)$ at the given $x .…

02:05

Find the equation of the tangent line to the graph of $f(x)$ at the indicated $…

01:56

Find $f^{\prime}(x)$ and the equation of the line tangent to the graph off at t…
Additional Mathematics Questions

01:16

What is the correct answer?
Thanks

Use geometry (not Riemann sums…

01:18

Determine whether the graph of the function provided is a graph of …

04:38

Find a polential function f for the field F
Fa (dy + 3z)i + (4x …

02:25

Evaluate the integral:
r3 + 6r + 2 dc

05:06

hotel chain typically charges $120 per room and rents average of 40 rooms Pe…

01:56

patient's pulse measures 80 bpm 130 bpm_ tnen 90 bpm_ To determine an a…

05:47


Consider the differential equation: 2y" + 18y = 6tan 3x …

01:30


Find all values x = where the function discontinuous For each…

03:18

Find the intervals on which ((x) is increasing, (he intervals on which ((x) …

05:22

Find the first four nonzero terms of the Taylor series for the func…

Add To Playlist

Hmmm, doesn't seem like you have any playlists. Please add your first playlist.

Create a New Playlist

`

Share Question

Copy Link

OR

Enter Friends' Emails

Report Question

Get 24/7 study help with our app

 

Available on iOS and Android

About
  • Our Story
  • Careers
  • Our Educators
  • Numerade Blog
Browse
  • Bootcamps
  • Books
  • Notes & Exams NEW
  • Topics
  • Test Prep
  • Ask Directory
  • Online Tutors
  • Tutors Near Me
Support
  • Help
  • Privacy Policy
  • Terms of Service
Get started