Problem

If $ F(x) = f(g(x)), $ where $ f(-2) = 8, f'(-2) …

01:10

Question

Answered step-by-step

Problem 60 Hard Difficulty

At what point on the curve $ y = \sqrt {1 + 2x} $ is the tangent line perpendicular to the line $ 6x + 2y = 1? $

Video Answer

Solved by verified expert

Textbook Answer

Official textbook answer

Video by Heather Zimmers

Numerade Educator

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

November 15, 2020

Thank you!! You teach at Oregon State?

Top Calculus 1 / AB Educators

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

Problem 87

Problem 88

Problem 89

Problem 90

Problem 91

Problem 92

Problem 93

Problem 94

Problem 95

Problem 96

Problem 97

Problem 98

Problem 99

Problem 100

Video Transcript

in this problem. We're looking for the point where the Tanja line is perpendicular to the given line and perpendicular lines have opposite reciprocal slopes. So let's find the slope of the given line. Let's take this equation and isolate why. So we'll subtract six x from both sides and divide by two. So the slope of this line is negative. Three. So the perpendicular slope would be positive 1/3. So we're looking for the point where the Tanja line has a slope of 1/3. That means we want the derivative to equal 1/3. So let's find the derivative. I'm going to rewrite the function as one plus two x to the 1/2 power and then I'm going to use the chain rule. Why Prime equals 1/2 times one plus two x to the negative 1/2 power that takes care of the first part of the chain rule times the derivative of the inside, which is to now we can multiply the 1/2 of the two that was canceled. And now we want this derivative to be equal to 1/3 so this derivative could be written as one over the square root of one plus two x, and it equals 1/3. Let's take the reciprocal of both sides, and we have a square root of one plus two. X is equal to three. Now it's square both sides, and we have one plus two. X equals nine. Subtract 12 X equals eight and divide by two. X equals four. Okay, this is the X coordinate of the point. We also want the Y coordinate of the point, and the Y coordinate would be what we get when we take four and substituted into the original equation. So we have one plus two times for inside a square root square root of nine is three. So the point we're looking for is the 0.0.43

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.

Problem

If $ F(x) = f(g(x)), $ where $ f(-2) = 8, f'(-2) …

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

More Answers

Related Courses

Calculus: Early Transcendentals

Related Topics

Discussion

Top Calculus 1 / AB Educators

Anna Marie Vagnozzi

Caleb Elmore

Kristen Karbon

Michael Jacobsen

Calculus 1 / AB Courses

Recommended Videos

Watch More Solved Questions in Chapter 3

Video Transcript

James Stewart

Calculus: Early Transcendentals

Anna Marie Vagnozzi

Caleb Elmore

Kristen Karbon

Michael Jacobsen

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

Calculus: Early Transcendentals

Anna Marie Vagnozzi

Caleb Elmore

Kristen Karbon

Michael Jacobsen

James StewartCalculus: Early Transcendentals

Anna Marie Vagnozzi

Caleb Elmore

Kristen Karbon

Michael Jacobsen

James Stewart

Calculus: Early Transcendentals