Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

bluebird Group Title

Would someone please explain how to find the inflection point, y"=0, of the equation y"= -2[4x^3-15x^2+12x-5]/(1-x^2)^3 without a graphing calculator, please?

  • one year ago
  • one year ago

  • This Question is Closed
  1. Shini Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    You already have the second derivative of the function so all you have to do is set the equation equal to 0 and then solve it. This will give you possible points of inflexion. Then you check the concavity of the point found by substituting the x-values one higher then the x-value you found and one lower. If you get a positive on one side and a negative on the other (doesn't matter which) you have found a point of inflexion.

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

    so is it like this? \[0=\frac{ -2\left[ 4\chi ^{3}-15\chi ^{2}+12\chi -5 \right] }{ \left( 1-\chi ^{2} \right)^{3} }\] But how do you start to solve it?

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

    \[-2[4x^3 -15x^2 + 12x - 5] = 0\] \[4x^3 - 15x^2 + 12x -5 = 0\] Then solve it from there

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

    okay so I got: \[\chi \left( 4\chi ^{2}-15\chi +12 \right)=5\] then I used the \[\frac{ -b \pm \sqrt{b ^{2}-4ac} }{ 2a }\] and got 2.593070331 and 1.156929669. So do I put those numbers in the equation and test if they equal to 0?

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

    There is also the value of x = 5. When you used the quadratic formulas to find the x-values did you first separate the equation you got into: \[x = 5, 4x^2 - 15x + 12 = 5\] If not, try that. Were you given the original equation? If you were you substitute the values you got into that to get the possible points. If not don't worry. After that i usually check if the concavity changes by drawing: |dw:1358129096454:dw| and then repeat that for the rest of the x values you got. Sorry im not being a great deal of help anymore, if anything im confusing you more.

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

    the original equation was \[y =\frac{ 2\chi ^{2}-4\chi +3 }{ 1-\chi^{2} }\] and I got, When X=4 Y=0.21007 When X=6 Y= 0.05133

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

    I mean Y" oops.

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

    I still can't find the inflection point...

    • one year ago
  9. wio Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Ummm still need help?

    • one year ago
  10. wio Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Since you have an equation of degree 3, you need to find one of the roots first without the help of the quadratic equation.

    • one year ago
  11. bluebird Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    The there is another way to find it?

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

    *then

    • one year ago
  13. wio Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Well you sort of have to guess.

    • one year ago
  14. wio Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    What is the equation we want to find the roots of exactly?

    • one year ago
  15. wio Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Which function exactly is \(y''\). I see a lot of functions here.

    • one year ago
  16. wio Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    @bluebird Please?

    • one year ago
  17. bluebird Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    sorry about that... the first one equation in the question is y". I need to find the inflection point for y"=0

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

    \[y"=\frac{ -2\left[ 4\chi ^{3}-15\chi ^{2}+12\chi -5 \right] }{ \left( 1-\chi ^{2} \right)^{3} }\] to be exact

    • one year ago
  19. wio Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Um ok still here?

    • one year ago
  20. wio Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    First thing to notice is that it's undefined at 1 and -1. Next thing to notice is that if the numerator (part on top) is 0, then the whole thing is 0. So we can ignore the denominator as long as we keep the first thing in mind.

    • one year ago
  21. wio Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    I'd start by just distributing that \(-2\). There's not reason to have that factored out.

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

    oh okay... so it's only the \[-2\left[ 4\chi ^{3}-15\chi ^{2}+12\chi -5 \right]\] part I work with right?

    • one year ago
  23. wio Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Yes. Ultimately we could multiply both sides by the denominator, and since the other size is 0, it would remain 0.

    • one year ago
  24. wio Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    I suppose you could get rid of that \(-2\) with the same logic.

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

    \[-4\chi^{3}-15\chi ^{2}+12\chi -5\] is not factor-able right?

    • one year ago
  26. wio Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    why is there a negative in front of the 4?

    • one year ago
  27. bluebird Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    oh oops i mean 4

    • one year ago
  28. wio Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    yeah apparently it has a really nasty real root, and two imaginary roots.

    • one year ago
  29. wio Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Did they give you y'' or y originally?

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

    they gave me y originally and I was suppose to sketch the graph and find the inflection points without a graphing calculator

    • one year ago
  31. wio Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    What was y?

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

    \[y=\frac{ 2\chi ^{2}-4\chi +3 }{1-\chi ^{2} }\]

    • one year ago
  33. wio Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Oh wow, what was y'?

    • one year ago
  34. wio Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Why were you opposed to just graphing it?

    • one year ago
  35. bluebird Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    \[y'=\frac{ -4\chi ^{2}+10\chi -4 }{ \left( 1-\chi ^{2} \right)^{2} }\]

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

    you mean graph it with a calculator or by hand?

    • one year ago
  37. wio Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    by hand

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

    I have to label the inflection points and I can't find the y"=0 one

    • one year ago
  39. wio Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    The only way to really find it is to use the very erudite formula for 3rd degree polynomials, or use some other root finding method.... like Newton's method.

    • one year ago
  40. wio Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    or bisection

    • one year ago
  41. bluebird Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    I don't know the other methods....

    • one year ago
  42. wio Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    http://en.wikipedia.org/wiki/Cubic_function#General_formula_of_roots The formula is HUGE

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

    I'm not sure if i can memorize that....

    • one year ago
  44. wio Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Seems like the only thing you could really do is to

    • one year ago
  45. wio Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    graph it and then plug in points really close to the inflection point

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

    oh okay... so I can just guess the inflection point then, right?

    • one year ago
  47. wio Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    yeah. The problem seems kinda messed up.

    • one year ago
  48. wio Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    You can sort of see how the tangent line would intersect between 2 and 3

    • one year ago
  49. bluebird Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Okay, thank you so much for your help!

    • one year ago
    • Attachments:

See more questions >>>

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.