Problem

For what values of $ a $ and $ b $ is the line $ …

00:51

Question

Answered step-by-step

Problem 76 Hard Difficulty

Suppose the curve $ y = x^4 + ax^3 + bx^2 + cx + d $ has a tangent line when $ x = 0 $ with equation $ y = 2x + 1 $ and tangent line when $ x = 1 $ with equation $ y = 2 - 3x. $ Find the values of $ a,b,c, $ and $ d. $

Video Answer

Solved by verified expert

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

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

he is clear. So when you read here, so we have why is equal to x square plus a X cubed plus B x square class C X plus t you have are given and we're gonna substitute X is equal to zero and why is equal to one? When we get into this equation and we get a d value of one were given that why is equal to two minus three x is attention Xs equal to one the y cornett when xs equal to one gives a Y value of negative one. So we see that one common negative one lies on the curb. So we're gonna substitute it into our main equation and we get negative too is equal to a plus B plus C plus de when we substitute t equals one. Yet negative three is equal to a plus B plus c Next we're going to difference. She our equation and we got d Y over DX is equal to four x cute plus three a x square plus to be explicit. See, it s stated that why equals two x plus one is a tangent at X equals two. So the slur slope of the curve at X equals two X equals zero is too. So we're gonna substitute two and we gotta see value of two and were given that like we stated before, why is equal to two minus three axes? A tangent at X equals one. So the slope of the curve X equals one is negative three. So we're also gonna substitute, do you? Why? Over D X is equal to negative three and X is equal to one. We get negative. Three is equal to four times one cubed plus three a one square plus to be terms one plus c. Then we get negative. C is equal to three a plus two three plus c When we substitute c last two and we get negative five is equal to a crust Be we're substituting it into the equation. Negative three plus a plus B plus c. So after we substitute to, we're gonna substitute to in our equation. Negatives. Seven equals three a plus two b plus C When we get negative. Nine as people 23 a plus two b When we get negative, 4.5 is equal to 1.5 a plus B and we're gonna substitute this with We're going to subtract thes two equations when we get you're me as one and we're going to substitute a equals one into negative five is equal to a plus B to get a B value of negative six. So after all this, we get our A, B, C and D values. And we're going to just grab this right here, just confirm our answer. Look, something like this guesses one common negative one and zero common one on our equation becomes why is equal to X to the fourth plus X Cube minus six square was two x plus one.

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

For what values of $ a $ and $ b $ is the line $ …

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

Catherine Ross

Anna Marie Vagnozzi

Heather Zimmers

Caleb Elmore

Calculus 1 / AB Courses

Recommended Videos

Watch More Solved Questions in Chapter 3

Video Transcript

James Stewart

Calculus: Early Transcendentals

Catherine Ross

Anna Marie Vagnozzi

Heather Zimmers

Caleb Elmore

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

Calculus: Early Transcendentals

Catherine Ross

Anna Marie Vagnozzi

Heather Zimmers

Caleb Elmore

James StewartCalculus: Early Transcendentals

Catherine Ross

Anna Marie Vagnozzi

Heather Zimmers

Caleb Elmore

James Stewart

Calculus: Early Transcendentals