A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • 5 years ago

Consider the function f(x,y)=5x−9y+4xy−7(x^2)+6(y^2) defined in the unit square 0</=x</=1, 0</=y</=1. Find the maximum and minimum values of f and where they occur.

  • This Question is Closed
  1. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    it appears to be hyperbolic ......

  2. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    we can get a vector derivative if we take the gradient: but I aint sure how that would help yet

  3. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    f(x,y)=5x−9y+4xy−7(x^2)+6(y^2) fx(x,y) = 5 +4y -14x fy(x,y) = -9 +4x +12y

  4. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    gf = (5 +4y -14x , -9 +4x +12y) can also define the normal to the surface; when this is pointing straight up or down would give you a tangent plane for a min or max right?

  5. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    straight up is the same as (0,y); so id say make x=0 for starters ... just a hunch

  6. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    gf = (5 +4y , -9 +12y)

  7. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    nice multivariable

  8. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    that mighta been a wrong step lol

  9. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    aint it tho :)

  10. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    gf = (5 +4y -14x , -9 +4x +12y) maybe when 5 +4y -14x = 0

  11. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I don't remember how to do this.. but we dealing with a gradient mic in one of my classes

  12. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    mic check one two one two

  13. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    5 +4y -14x = 0 y = 14x-5 x = 4y +5 ----- ------ 4 14

  14. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    can you use LaTeX here?

  15. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    you can \(\try\)

  16. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    when: 5 +4y -14x = -9 +4x +12y we might get a zero derivative.... 5 + 4y -14x 9 -12y -4x ----------- 14 -8y -18x = 0 18x +8y = 14 ... i wonder...

  17. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    http://www.wolframalpha.com/input/?i=5x%E2%88%929y%2B4xy%E2%88%927%28x^2%29%2B6%28y^2%29

  18. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i was sooo close lol add the gradient parts and do something....

  19. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i was on the right track; when the x and y parts of the gradient =0 we got a tangent plane that is flat.... to indicate a high and low

  20. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    18x +8y = 14; we can use values between 0 and 1 to find out what works now

  21. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    the line y=-(18x+14)/8 should give us the answers right? or y = -(9x+7)/4

  22. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    http://www.wolframalpha.com/input/?i=18x+%2B8y+-+14%3D0

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

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

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.