A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • one year ago

Find the equation of the line tangent to y = –x2 + 3x + 8 at x = 2.

  • This Question is Closed
  1. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @dan815 could you help me?

  2. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    the derivative formula that I got is f'(x)= -6x+1

  3. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    but none of the answers match my answer

  4. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Find the equation of the line tangent to y = –x2 + 3x + 8 at x = 2. y = –2x + 2 y = –x + 12 y = –x + 2 y = –2x – 12

  5. dan815
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    |dw:1436827395674:dw|

  6. dan815
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    |dw:1436827520119:dw|

  7. dan815
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    y = –x + 12

  8. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    is it 26

  9. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    could you explain me how you got that answer

  10. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @dan815

  11. dan815
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    did you get the derivative function right

  12. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yes, because when I plug the value of 2 into my formula I get -1, which you presented me that it was correct, but I don't know how you got that formula

  13. dan815
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    f'(x)= -6x+1 you said you got this, something wrong there

  14. dan815
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    you have to differentiate term by term

  15. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    never mind I got -2x+3

  16. dan815
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    okay

  17. dan815
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    now you have a slope, then you find a point that belongs on this tangent line

  18. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    but that doesn't have anything in common to the other answers

  19. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    how?

  20. dan815
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    |dw:1436828112090:dw|

  21. dan815
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    we know the x coordinate of the point,

  22. dan815
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    now we find the y coordinate of the point and its part of the parabola so

  23. dan815
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    y(2) = ?

  24. dan815
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    |dw:1436828189830:dw|

  25. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    do we plug it into the original formula or the derivate one?

  26. dan815
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    we have the slope there, now we need to find the y coordinate then you will have a point and a slope and you figure out the equation of the line

  27. dan815
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    the derivative formula only tells you the slope at every x value

  28. dan815
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    we want to know the actual y point

  29. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so which formula could I use to find the y value?

  30. dan815
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    think about it

  31. dan815
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    the tangent line intersects one point on the parabola, at x=2 and y is something, we can always find the y value for every x value on a parabola how?

  32. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    maximum

  33. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    wait no, OMG I feel so ignorant.

  34. dan815
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    y = –x^2 + 3x + 8 this equation of parabola

  35. dan815
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    it gives you a y value for every x value

  36. dan815
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    we know there is an intersection at x=2 so we have to see the y value there

  37. dan815
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    y = –x^2 + 3x + 8 y=-2^2+3*2+8 = 10

  38. dan815
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    x=2,y=10 (2,10)|dw:1436828495281:dw|

  39. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I got 10

  40. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yes,

  41. dan815
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    now u have a point at the slope of the tangent line through that point

  42. dan815
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    can you solve the equation of the line from here

  43. dan815
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    y=mx+b m=-1 lets plug in our point to see what b or the y intercept must be 10=-1*2+b b=

  44. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    9

  45. dan815
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    10=-1*2+b 10=-2+b b=10+2=12

  46. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Oh i see I thought it was a 1 to the second power

  47. dan815
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    this is the equation of a line y=mx+b

  48. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yeah, OMG I got it. Thank you so much. Could you help me with one more and thats it?

  49. dan815
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    yeah sure

  50. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

  51. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I already found that C actually has the value, but I don't know how to solve A nor B

  52. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @dan815

  53. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @phi

  54. dan815
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    |dw:1436829534343:dw|

  55. dan815
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    this is the definition of a derivative

  56. dan815
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    it is the equation to find the slope of a tangent line at x

  57. dan815
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    it arises from taking a secant line where the points are getting closer and closer, lim h--->0

  58. dan815
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    for example take a look at any function f(x)

  59. dan815
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    |dw:1436829711928:dw|

  60. dan815
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    suppose you want to find the derivative at that point x for this function, you can begin to approximate by taking points close to that value because that is a close linear approximation

  61. dan815
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    |dw:1436829768720:dw|

  62. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    okay, I see. I got 7 as the slope of the function

  63. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    at x=2

  64. dan815
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    |dw:1436829791039:dw|

  65. dan815
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    if we keep making h smaller and smaller then the point is close and closer to the actual tangent slope

  66. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    which is 7 right?

  67. dan815
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    |dw:1436829918175:dw|

  68. dan815
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    well my work is done as long you understand how a derivative comes

  69. dan815
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    its from this very simple concept, the slope of the tangent line at some point

  70. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    okay than you, I understood the secant and tangent line more.

  71. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.