Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

Christos

  • one year ago

Graphs and functions/derivatives, Hey can you help me with this? http://screencast.com/t/MVj3e9Ok2Yg0

  • This Question is Closed
  1. .Sam.
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 3

    \[p(x)=(x+1)^2(2x-x^2)\] From there, you can tell that (x+1)=0, x=-1 is a zero of p(x) Then factor this \((2x-x^2)\) and set the brackets equals zero and find the other 2 zeros

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

    its -1 0 and 2

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

    Oh so thats the first step

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

    Yup |dw:1369655367345:dw|

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

    Now, differentiate p(x), set it equals to zero to find the maximum and minimum points

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

    its -4x^3+6x+2 if I am not mistaken we take x=0 and x=+-sqrt(3)/sqrt(2)

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

    Yeah, set -4x^3+6x+2 equals zero and solve for x

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

    yea I solved for x and I got 3 roots x=0 and x=+-sqrt(3)/sqrt(2) are my calculations correct??

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

    Hmm, \[-4x^3+6x+2 \\ \\ -2(2x^3-3x-1) \\ \\ -2(x+1)(2x^2-2x-1)\] Factoring \(2x^2-2x-1\) you get \[x=\frac{1}{2} \left(1-\sqrt{3}\right)~~~~~,~~~~~\frac{1}{2} \left(1+\sqrt{3}\right)\] These x are the max and min points of the graph, then use these x substitute into \[y=(x+1)^2(2x-x^2)\] Find the y's

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

    hmm how did you get from line 2 to line 3?

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

    http://screencast.com/t/yNU8TQxrMkn this here

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

    I used trial an error with calculator, when \[p(-1)=-2(2(-1)^3-3(-1)-1)=0\] Then (x+1) is a factor of p(x), then use (x+1) divide \((2x^3-3x-1)\)

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

    oh ok lets find the ys

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

    y = 0 ?

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

    I subtitute with 0 or the roots?

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

    Substitute these \(x=\frac{1}{2} \left(1-\sqrt{3}\right)~~~~~,~~~~~\frac{1}{2} \left(1+\sqrt{3}\right)\) into \(y=(x+1)^2(2x-x^2)\)

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

    Then that's the coordinates of max and minimum points

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

    that was really long to find wasnt it? I tried to find the first one and I found (-2 + sqrt(3))/2 which seems to be wrong here

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

    Yeah It's abit long For \(x=\frac{1}{2} \left(1-\sqrt{3}\right)\) or -0.3660, \[y=(x+1)^2(2x-x^2)\] \[y=(\frac{1-\sqrt3}{2} +1)^2(2(\frac{1-\sqrt3}{2})-(\frac{1-\sqrt3}{2})^2)\] \[y=\frac{9-6\sqrt{3}}{4}~~or-0.348\]

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

    ok I see

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

    (-0.3660,-0.3481) Then for the other coordinate is (1.366,4.848)

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

    ok

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

    Now that we know those coordinates how can we use them?

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

    Yup |dw:1369657703814:dw|

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

    Then the coefficient of highest degree is negative so the graph curves down|dw:1369657774047:dw|

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

    And yeah, zeros are -1 0 and 2, why am I plotting 1 for.

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

    hmm are you plotting it to get an estimation of the infliction point?

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

    Yup

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

    or else you won't know where it changes it's direction

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

    I see , is there anything else left for this graph/exersise?

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

    That's it

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

    Thanks :) I will try to solve some on my own now, if I have any problem can I tell you?

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

    I'll try :)

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

    ok

  35. 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.