Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

mathcalculus

  • one year ago

PLEASE HELP :( !! y=13e^(3x^2)-6x at x=3 in the form y=mx +b has

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

    f'(x)= 78xe^(3x^2)-6

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

    slope= 234e^27-6 y=13e^27-18

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

    So you're looking for an equation of the line tangent to the curve f(x) at x=3?

  4. akotto4897
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    omg this is so simple

  5. akotto4897
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    wat is america coming to

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

    yes, Determine the equation of the line tangent to the graph of

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

    yeah but I'm not sure why I'm getting this wrong.

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

    @akotto4897 wtf is wrong with you? Why would you call someone elses problem `so simple`. It's like someone in 5th grade calling 3rd grade math SUPER EASY! Just because you understand it doesn't mean that everyone else is on your level...

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

    Ok that's enough of my rant :) lemme check your work a sec :3

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

    lol, i appreciate that. but yes, let's begin.

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

    Mmm ok so your slope looks good. So what coordinate pair are we using to find our y-intercept?\[\Large f(3)\quad=\quad 13e^{27}-18\]Mmm ok ok I see you have the written down already :3 \[\Large y_{\tan}\quad=\quad mx+b\]So if we plug in our coordinate pair, we get something like this, yes?\[\Large 13e^{27}-18\quad=\quad (234e^{27}-6)\cdot 3+b\]

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

    woah so the slope is good and the y too.

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

    oh i see there's an x there.

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

    so would it be 247e^27-18?

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

    for your y_tan? or for b?

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

    y tan

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

    Hmm after you find your b value, you should plug it back into the \[\Large\bf y_{tan}\quad=\quad \color{royalblue}{m}x+\color{royalblue}{b}\] For our final answer, we DON'T want the coordinate pair plugged in. We're only trying to fill in these blue pieces.

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

    so how do i get to the answer.

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

    at first i thought it was 247e^27 -6x

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

    grr sorry website crashed on me >:c

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

    its fine

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

    i just don't understand what to do at the point slope formula.

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

    i keep getting the answer wrong.

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

    \[\Large\bf y_{\tan}\quad=\quad \color{royalblue}{m}x+\color{royalblue}{b}\]Plugging in our slope,\[\Large\bf y_{\tan}\quad=\quad \color{royalblue}{(234e^{27}-6)}x+\color{royalblue}{b}\]Then we plug in our coordinate pair to find b,\[\Large\bf \color{#DD4747 }{13e^{27}-18}\quad=\quad \color{royalblue}{(234e^{27}-6)}\cdot\color{#DD4747 }{3}+\color{royalblue}{b}\]

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

    So we have some -18's cancelling out. And I think we get a b value of,\[\Large\bf \color{royalblue}{b\quad=\quad -689e^{27}}\]Something like that?

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

    isn't it y-(13e^27-18)=234e^27-6x+18

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

    y-?

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

    right, y-y1=m(x-x1)

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

    so in this case, slope= 234e^27-6 y=13e^27-18

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

    and x1= 3

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

    No that's `point-slope` form of a line. y-y1 = m( x-x1) We don't want to use that. We were told to use the `slope-intercept` form of a line. y=mx+b

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

    can we do it the way i had it please?

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

    yeah but i thought i could use that to find the equation of a tangent line

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

    I've been using that for other problems and it worked.

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

    Yes we can use that, so let's see if we can get it set up correctly. Lemme see if I can match what you wrote a sec :)

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

    ok

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

    \[\Large\bf y-y_1\quad=\quad \color{royalblue}{m}(x-x_1)\]\[\Large\bf y-y_1\quad=\quad \color{royalblue}{(234e^{27}-6)}(x-x_1)\]Then plugging in our point:\[\Large\bf y-\color{#DD4747 }{(13e^{27}-18)}\quad=\quad \color{royalblue}{(234e^{27}-6)}(x-\color{#DD4747 }{3})\]

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

    yes correct! :)

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

    after that I'm lost lol

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

    Ok so now we just need to get in into the form y=mx+b. So we need to multiply out the brackets, then we gotta isolate the y term.

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

    \[\large\bf y-\color{#DD4747 }{(13e^{27}-18)}\quad=\quad 234e^{27}x-6x -702e^{27}+18\]I think it expands like that, yes? Give it a try :)

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

    yup, but i seem to be doing that wrong unfortunately.

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

    wait don't we just multiply out the -6 and -6*-3 only?

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

    and leave the

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

    Yes, true. We probably want don't want the x's expanded like that,\[\large\bf y-\color{#DD4747 }{(13e^{27}-18)}\quad=\quad (234e^{27}-6)x -702e^{27}+18\]

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

    \[\Large 234e^{27}\cdot-3\]

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

    why don't we multiply 234e^27 with x?

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

    and then -3

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

    \[\large\bf (234e^{27}-6)(x-3)\quad=\\ \large\bf\quad (234e^{27}-6)x-(234e^{27}-6)3\]And we only want to multiply out the part with the 3.

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

    im so confused. i do't understand why we did this problem differently than all the others when it comes to this part.

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

    so for (234e^27−6)(x−3) i thought we do foil

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

    Yes, foiling should give you this,\[\large\bf 234e^{27}x-6x -702e^{27}+18\]

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

    Are you not getting that when you foil..?

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

    yes i have that! :)

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

    We don't want multiple x terms, so we'll factor an x out of each of the first two terms.\[\Large\bf =\quad \large\bf (234e^{27}-6)x -702e^{27}+18\]

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

    now what? :(

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

    where does my foiling go?

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

    great so we factor?

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

    We had this,\[\Large\bf y-\color{#DD4747 }{(13e^{27}-18)}\quad=\quad \color{royalblue}{(234e^{27}-6)}(x-\color{#DD4747 }{3})\]It foiled to give us this,\[\large\bf y-(13e^{27}-18)\quad=\quad 234e^{27}x-6x -702e^{27}+18\]We factored out an x to give us this,\[\large\bf y-(13e^{27}-18)\quad=\quad (234e^{27}-6)x -702e^{27}+18\]

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

    We finish by solving for y.

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

    right

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

    x(-468+12)

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

    \[\large\bf y=\\\large\bf (234e^{27}-6)x -702e^{27}+18+13e^{27}-18\]

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

    what..? :(

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

    the -6 and the 18 are not like terms, we can't combine those.

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

    I don't know why you insisted on using point-slope form for this one. It seems way more complicated :c

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

    but it's the only way for me… i have to stick to this or else i'll be completely lost in the exam

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

    This one only ended up being complicated because our slope was `2 terms`. So it ended up being a ton of multiplication.

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

    damn im so confused.

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

    =[

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

    what would be he answer btw?

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

    \[\large\bf y-(13e^{27}-18)\quad=\quad (234e^{27}-6)x -702e^{27}+18\]From here: you add (13e^{27}-18) to each side,\[\large\bf y=\\ \large\bf(234e^{27}-6)x -702e^{27}+18\color{orangered}{+(13e^{27}-18)}\]Does that step make sense? +_+ That's how we isolate the y term.

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

    From there we can drop the brackets since nothing in being applied to them, \[\large\bf y=\\ \large\bf(234e^{27}-6)x -702e^{27}+18+13e^{27}-18\]It looks like the 18's will cancel out,\[\large\bf y=\\ \large\bf(234e^{27}-6)x -702e^{27}+\cancel{18}+13e^{27}-\cancel{18}\]

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

    And the exponential terms ( not the one attached to the x ) are like terms, so we'll combine them,\[\large\bf y=\\ \large\bf(234e^{27}-6)x \color{orangered}{-702e^{27}+13e^{27}}\] \[\large\bf y=(234e^{27}-6)x \color{orangered}{-689e^{27}}\]And I think that's our final answer, assuming I didn't make any boo boos along the way.

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

    wait which is the mx and b?

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

    oh it is correct….

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

    \[\large\bf y=\color{royalblue}{(234e^{27}-6)}x \color{orangered}{-689e^{27}}\]\[\large\bf y=\color{royalblue}{m}x +\color{orangered}{b}\]

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

    • Attachments:

Ask your own question

Ask a Question
Find more explanations on OpenStudy

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.