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

Sketch the parabolas $ y = x^2 and $ y = x^2 - …

03:40

Question

Answered step-by-step

Problem 85 Hard Difficulty

If $ c > \frac {1}{2}, $ how many lines through the point (0, c) are normal lines to the parabola $ y = x^2? $ What if $ c \le \frac {1}{2}? $


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

02:31

Frank Lin

Related Courses

Calculus 1 / AB

Calculus: Early Transcendentals

Chapter 3

Differentiation Rules

Section 1

Derivatives of Polynomials and Exponential Functions

Related Topics

Derivatives

Differentiation

Discussion

You must be signed in to discuss.
Top Calculus 1 / AB Educators
Catherine Ross

Missouri State University

Heather Zimmers

Oregon State University

Caleb Elmore

Baylor 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

05:36

If $c>\frac{1}{2},$ how…

04:23

Where does the normal line…

01:05

The graph shows the normal…

08:38

Normals to a Parabola The …

22:04

Normals to a Parabola The …

01:20

Find equations of lines wh…

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
Problem 65
Problem 66
Problem 67
Problem 68
Problem 69
Problem 70
Problem 71
Problem 72
Problem 73
Problem 74
Problem 75
Problem 76
Problem 77
Problem 78
Problem 79
Problem 80
Problem 81
Problem 82
Problem 83
Problem 84
Problem 85
Problem 86

Video Transcript

I can't square. So when you right here. So we have Why is equal to X square? This is our given function. We're gonna differentiate it to get this slope off the tangent and we have two X We have the cornet zero comma SSI just given to us. The normal line is the line perpendicular to the tangent line. So we have to find a point or the tangent line passes. So we make X equal to a When we get the point A comma a square on the slope of the tangent line is too late. We have Where next? Gonna find the normal line, which is the perpendicular line on the slope is the negative reciprocal of the tension Learn slope So we get them off. The normal line is equal to negative one over, Um and this is equal to negative one over two A. So, after we find are a normal mind slow. We have the cornet points, that pastor, the tangent line and the normal line So we can now plug it in. We get why too minus y one over x two minus x one is equal to negative one over two a we plug it in a square. Runa C. Over a minute zero is equal to a negative one over two A. You'll get a square is equal to C minus 1/2. So if C is equal to one, have that means A is going to be equal to zero. So we get a square is equal to 1/2 minus one have is equal to zero. So there's only one solution. If see, it's bigger than zero and there are a can be positive or negative square root of seeing minus 1/2. So there are two solutions. And if C is less than 1/2 there is no solution. We're gonna drop her if we look at our parabola here. CIA's bigger, then 1/2. There are three normal lines, including the lie axis, and when C is less than or equal to negative 1/2 there's only one solution, and that's when C is equal to 1/2

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
65
Hosted by: Ay?Enur Çal???R
Math (Algebra 2 & AP Calculus AB) with Yovanny
Arrow icon
Participants icon
43
Hosted by: Alonso M
See More

Related Topics

Derivatives

Differentiation

Top Calculus 1 / AB Educators
Catherine Ross

Missouri State University

Heather Zimmers

Oregon State University

Caleb Elmore

Baylor 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

05:36

If $c>\frac{1}{2},$ how many lines through the point $(0, c)$ are normal lines …

04:23

Where does the normal line to the parabola $ y = x^2 - 1 $ at the point (-1, 0…

01:05

The graph shows the normal lines from the point (2,0) to the graph of the parab…

08:38

Normals to a Parabola The graph shows the normal lines from the point $(2,0)$ t…

22:04

Normals to a Parabola The graph shows the normal lines from the point $(2,0)$ t…

01:20

Find equations of lines whose graphs intersect the graph of the parabola $y=x^{…
Additional Mathematics Questions

02:48

'Find the slope of the line tangent to
y5 +3x2y2 +x3 = 21 at (2, 1) …

03:11

'The sonar of navy cruiser detects submarine that is 4000 feet from the…

03:37

'An insurance COmpany looks at the records for millions of homeowners a…

01:08

'Find the mean; |, for the binomial distribution #hich has the stated v…

01:35

'A tennis player makes a successful first serve 51% of the time If she …

01:33

'Find the standard deviation, 0, for the binomial distribution which ha…

00:50

'STATE: How heavy load (in pounds) is needed to pull apart pieces of Do…

03:30

'camied from & mine in West Virginia t0 a power plant In New York I…

00:36

'Jeremy draws an equilateral triangle If he draws a line of symmetry th…

04:33

'A $25 000, 10% bond redeemable at par on December 1, 2025,is purchased…

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
  • Topics
  • Test Prep
  • Ask Directory
  • Online Tutors
  • Tutors Near Me
Support
  • Help
  • Privacy Policy
  • Terms of Service
Get started