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

Snowflake123 Group Title

Not sure how to do this: Please explain??? :D Write down the set of values of the constant k for which the equation 2X^3-3X^2-12X-7=k has exactly one real solution. Thanksss

  • 2 years ago
  • 2 years ago

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

    nice drawing :P

    • 2 years ago
  2. Snowflake123 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    isnt it finding a value for k????

    • 2 years ago
  3. mukushla Group Title
    Best Response
    You've already chosen the best response.
    Medals 4

    lol...tnx so for any real number \(k\) there is exactly one solution for the equation see the intersects of horizental lines and \(f(x)\)

    • 2 years ago
  4. SNSDYoona Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    why do u differentiate the equation ?

    • 2 years ago
  5. mukushla Group Title
    Best Response
    You've already chosen the best response.
    Medals 4

    |dw:1345805312784:dw|

    • 2 years ago
  6. mukushla Group Title
    Best Response
    You've already chosen the best response.
    Medals 4

    because i want to see what is the behaviour of function

    • 2 years ago
  7. mukushla Group Title
    Best Response
    You've already chosen the best response.
    Medals 4

    if it was something like this|dw:1345805467267:dw| for some values between \(k_1\) and \(k_2\) there is more than one real root

    • 2 years ago
  8. mukushla Group Title
    Best Response
    You've already chosen the best response.
    Medals 4

    so i differentiate it to see if there is some critical points like last drawing or not.

    • 2 years ago
  9. Snowflake123 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    so is the answer k=all real numbers?

    • 2 years ago
  10. mukushla Group Title
    Best Response
    You've already chosen the best response.
    Medals 4

    i think yes...if im not wrong

    • 2 years ago
  11. mukushla Group Title
    Best Response
    You've already chosen the best response.
    Medals 4

    oops : misread : \[f(x)=2x^3−3x^2−12x−7\]\[f'(x)=6x^2-6x-12=0\]it gives \(x^2-x-2=0\) so \(x=-1,2\) so we have two critical points

    • 2 years ago
  12. mukushla Group Title
    Best Response
    You've already chosen the best response.
    Medals 4

    sorry @Snowflake123 ...

    • 2 years ago
  13. Mimi_x3 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    you sub the x back into the y for k i think..

    • 2 years ago
  14. mukushla Group Title
    Best Response
    You've already chosen the best response.
    Medals 4

    exactly

    • 2 years ago
  15. Snowflake123 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    so whats the k values

    • 2 years ago
  16. Mimi_x3 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    why not you try and sub it back in

    • 2 years ago
  17. Mimi_x3 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    sub it into y = 2x^2 - 3x^2 - 12x - 7

    • 2 years ago
  18. Mimi_x3 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    2x^3**

    • 2 years ago
  19. mukushla Group Title
    Best Response
    You've already chosen the best response.
    Medals 4

    so the graph will be like this|dw:1345806482815:dw| just try to work it out

    • 2 years ago
  20. Mimi_x3 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    why are there two k's?

    • 2 years ago
  21. mukushla Group Title
    Best Response
    You've already chosen the best response.
    Medals 4

    the equation \(f'(x)\) has 2 roots so there are 2 k's we must work it out

    • 2 years ago
  22. Mimi_x3 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    according to my notes dont you find the roots from the stationary points? so there is only one line \(y=k\)

    • 2 years ago
  23. mukushla Group Title
    Best Response
    You've already chosen the best response.
    Medals 4

    for \(k=k_1,k_2\) there are exactly 2 real roots for the equation \(f(x)=k\) for \(k_1<k<k_2\) there are exactly 3 real roots for the equation \(f(x)=k\)

    • 2 years ago
  24. mukushla Group Title
    Best Response
    You've already chosen the best response.
    Medals 4

    so the region we lookin for is \[k>k_2 \ \text{&} \ k<k_1 \]

    • 2 years ago
  25. mukushla Group Title
    Best Response
    You've already chosen the best response.
    Medals 4

    what do u mean by '' there is only one line y=k''

    • 2 years ago
  26. Mimi_x3 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    woops forget it i made a mistake; youre right

    • 2 years ago
  27. mukushla Group Title
    Best Response
    You've already chosen the best response.
    Medals 4

    lol...i hope im right...

    • 2 years ago
  28. Mimi_x3 Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    yes you are!! i just drew abit it differently so got kinda confused

    • 2 years 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.