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Find the max value of xy (done in a weird way)

  1. Mar 18, 2013 #1
    find the max value of xy (done in a "weird" way)

    1. The problem statement, all variables and given/known data
    so our teacher assigned this hw in the last 10 minutes
    we haven't read the function with 2 variables and i've never seen/used one
    (things were just getting in my head since it's only 10 mins i don't know if i'm making a mistake)
    suppose that x and y satisfie 4x+y=2
    find the maximum value of xy
    so this is done with deriviatives but i was thinking in using another way and it turned to be right , what i'm asking here is explaining why my method was right, anyway the answer is (1/4 , 1) this is how i've done it
    f(x)=4x+y-2 must be eqUAL TO 0
    f(xy)=4xy+y-2 this must be equal to 0( assumed that y is not changing i don't know )
    anyway this leads to x=2-y/4y
    replacing in 4x+y=2 we get y= 1 then x=1/4
    now our teacher used derviatives to solve this
    y=2-4x
    xy=2x-4x^2 etc and he gets the exact same answer as me , i don't think this is a coincidence so please explain to me why this is right , when i asked him he mentioned two variable functions..
    thanks everyone :)
     
    Last edited by a moderator: Mar 18, 2013
  2. jcsd
  3. Mar 18, 2013 #2

    Mark44

    Staff: Mentor

    Where did 4xy + y - 2 come from? In particular, the 4xy part.

    Edit: Now I see what you did, which was to substitute xy for x in the function definition. Even so, I'm not sure that what you did after that makes sense.
    What you wrote is x = 2 - (y/4 * y). Is that what you meant? Or did you mean x = (2 - y)/(4y)?
     
    Last edited: Mar 18, 2013
  4. Mar 19, 2013 #3
    Yes it doesn't look logical anyway thanks
     
  5. Mar 19, 2013 #4

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    This is incorrect. Because 4x+ y- 2= 0 for all x and y, if x changes, y must also change. In particular, you cannot write "f(x)= 4x+ y- 2" because f depends upon values of both x and y.

    Looks to me like shear coincidence. Your "method" is NOT valid.
     
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