Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

ranyai12

  • one year ago

Can someone please help!!! I keep getting it wrong!!! Find the extreme values of f(xy)=3x^2+2y^2−4x−3 on the region described as x^2+y^2 is less than or equal to 4

  • This Question is Closed
  1. harsimran_hs4
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    hey have you heard of langranges multipliers or not?

  2. ranyai12
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yea but i still got it wrong

  3. harsimran_hs4
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ok so can you show the working ...

  4. ranyai12
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yea this is what i did: f_x=6x-4<=4 6x<=8 x<=4/3 f_y=4y<=4 f_y<=1 fxx=6 fyy=4

  5. ranyai12
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    and then i got stuck so i assumed the max was 6 and min was 1

  6. ranyai12
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    but then i tried plugging in the values to the orginal equation and the number seemed wrong so idk what to do

  7. harsimran_hs4
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    firstly tell me that you want to proceed using concept of maxima minima using partial derivatives of langranges multipliers

  8. ranyai12
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    is there an easier way

  9. ranyai12
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    im good with anything

  10. harsimran_hs4
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    well perhaps i don`t think so because it`s gone in 2 dimension so lets do it by langranges multipliers 1. tell me what is gradient of f(x,y) ?

  11. ranyai12
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    fx=6x-4 fy=4y

  12. harsimran_hs4
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so that is (6x -4)i + (4y)j tell me the same for the boundary x^2 + y^2 = 4 also?

  13. ranyai12
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    im not sure im confused

  14. ranyai12
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    fx=2x and fy=2y

  15. ranyai12
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so 2xi and 2yj

  16. harsimran_hs4
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yes that is fine (2x)i + (2y)j so for extreme values to occur the gradient of the function and that of the boundary must be proportional so (6x -4)i + (4y)j = c((2x)i + (2y)j) now compare the i and j components and find the value of x and y in terms of c and tell me?

  17. ranyai12
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    sry im not exactly sure what you mean

  18. ranyai12
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    and whered the c come from

  19. harsimran_hs4
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    6x - 4 = 2cx and 4y = 2cy c is the proportionality constant better say the extreme values occurs when the gradient of two is antiparallel or proportional

  20. ranyai12
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so 2y=c

  21. ranyai12
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    3x=c+4

  22. ranyai12
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    im sry im not sure what to do now

  23. harsimran_hs4
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    x = 4/(6 - 2c) and c = 2 from second equation so x = 2 not the boundary x^2 + y^2 = 4 putting x = 2 and finding out value of y which come out to be 0 so (2, 0) is the point of extreme value

  24. ranyai12
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so 2 is the max and 0 is the min

  25. ranyai12
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    or do we plus in 2 into the equatio and thats hte max and 0 is the min

  26. harsimran_hs4
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    no the point (2, 0) will result in the extreme value of the function put x = 2 and y = 0 to yield the extreme value

  27. ranyai12
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    but wouldnt that result in just one value and not max and min

  28. ranyai12
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yr supposed to find absolute max and min and i got the answer ot be 1 which is wrong

  29. ranyai12
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @harsimran_hs4 did you get 1 as well

  30. harsimran_hs4
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yes perhaps then we screwed up with the calculation part can you tell me the answers if you have them with you?

  31. ranyai12
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    the answers arent given :(

  32. ranyai12
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    its an online hw thing

  33. harsimran_hs4
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ok then why did you say it`s wrong?

  34. ranyai12
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    because i plugged t in and it said it was wrong

  35. harsimran_hs4
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ok let me figure out then and i`ll get back to you

  36. ranyai12
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ok thanks

  37. harsimran_hs4
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    can you plug in -3 and check if thats minimum value?

  38. ranyai12
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    its not -3

  39. harsimran_hs4
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    do you get -ve points if you put in a wrong answer if no then check out if 9 is maximum or not

  40. ranyai12
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i only have one more try left to find out what the max and min is

  41. harsimran_hs4
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    then wait...

  42. harsimran_hs4
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    you need to plug in both the values simultaneously or not?

  43. ranyai12
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yea but i can still get partial pints

  44. harsimran_hs4
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    http://www.math.uri.edu/~bkaskosz/flashmo/graph3d/ check this this will give some insight to the problem but do link someone else also to this problem and figure out... i`ll try to get to some sure answer and then reply

  45. 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.