1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Maxima and Minima of a function of several variables

  1. Aug 17, 2013 #1
    1. The problem statement, all variables and given/known data

    Find the maxima and minima of:

    f(x,y)=(1/2)*x^2 + g(y)

    g∈⊂ (δ⊂ ℝ )

    in this region
    Ω={(x,y)∈ℝ2 / (1/2)*x^2 + y^2 ≤ 1 }

    hint: g: δ⊆ ℝ→ℝ

    The absolute min of f in Ω is 0
    The absolute max of f in Ω is 1

    2. Relevant equations



    3. The attempt at a solution

    I have the parameterization of the region: √2 *cosθ and senθ
    I also know ∇f(x,y)=(x,g`(y))=(0,0)
    x=0, g´(y)=0
    Hessian Matrix= [ 1 0
    0 g``(y) ]
    Determinat of the hessian matrix=g``(y)

    How can I complete this problem if I dont have the function g(y)?, how can I find g(y)?
     
  2. jcsd
  3. Aug 17, 2013 #2

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    What does that mean?

    The new parameter set is for the border of Ω only? For maxima/minima inside, I would keep x and y. It is easy to find a condition for x there.

    That is strange, indeed.
     
  4. Aug 17, 2013 #3
    I believe that means that g belongs to a subset of ℝ.

    Yes, the new parameter is just for the border.

    All the possible critical points would have to be (0,?). and ? being the result gotten from g`(y)=0, right?
     
  5. Aug 17, 2013 #4

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    I don't recognize "belongs to" as a mathematical term. g is certainly not a subset of ℝ, as it is a function ℝ→ℝ.

    Right, assuming g is differentiable.
     
  6. Aug 17, 2013 #5
    That`s what my teacher told me, but you are right it doesn´t make sense.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Maxima and Minima of a function of several variables
Loading...