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Maximum and Minimum Values Inside Triangle

  1. Oct 17, 2014 #1
    1. The problem statement, all variables and given/known data
    Find the absolute maximum and minimum values of f(x,y) = y^2+x^2 -4x + 11 on the set D where D is the closed triangular region with vertices (8,0),(0,4) , and (0,-4) .

    2. Relevant equations


    3. The attempt at a solution

    fx = 2x - 4
    fy = 2y

    Critical point = (2,0)

    The boundary of the triangle can be expressed in 3 lines, L1,L2, and L3. Find expressions for these lines.

    L1 : x=0 y[-4,4]
    L2 : y=-1/2x + 4 x[0,8]
    L3 : y=1/2x - 4 x[0,8]

    I checked the above, it is ALL correct.

    Along L1, f can be expressed by the one variable function:
    f = f(_,y) = ______
    Along L2, f can be expressed by the one variable function:
    f = f(x,_) = ______
    Along L3, f can be expressed by the one variable function:
    f = f(x,_) = ______

    I don't know what to put in the blanks above
     
  2. jcsd
  3. Oct 17, 2014 #2

    Mark44

    Staff: Mentor

    What's the x value along this vertical line?
    Given an x-value, how do you find the y value? You have the formula above.
    Given an x-value, how do you find the y value? You have the formula above
     
  4. Oct 17, 2014 #3

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    Just plug in the formulas for x you have for the individual lines.
     
  5. Oct 17, 2014 #4
    Thanks, solved!
     
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