Results 1 to 5 of 5

Math Help - Differentiation!!

  1. #1
    Member looi76's Avatar
    Joined
    Jan 2008
    Posts
    185

    Differentiation!!

    Question:
    The sum of two real numbers x and y is 12. Find the maximum value of their product xy.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Newbie
    Joined
    Feb 2008
    Posts
    10
    when x>=0 y>=0
    12=x+y>=2sqrt(x*y) (when x=y ,then x+y=2sqrt(x*y))
    so x*y<=(12/2)^2=36 ,when x=6 y=6 maximum value of x*y is 36
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Eater of Worlds
    galactus's Avatar
    Joined
    Jul 2006
    From
    Chaneysville, PA
    Posts
    3,001
    Thanks
    1
    I will stwp through this so you can see how to apply it to similar problems.

    This is a beginning max min problem. We have to maximize the product given

    that x+y=12.

    So, we have x+y=12 and xy must be maximum.

    Solve x+y=12 for, say, y. You easily get y=12-x

    Now, sub that into your product formula, xy

    x(12-x)

    This is what must be maximized. See, it has one variable now.

    Differentiate, set to 0 and solve for x. y will follow. See?.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member looi76's Avatar
    Joined
    Jan 2008
    Posts
    185
    galactus still don't know how you got x(12-x). can you please explain.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by looi76 View Post
    galactus still don't know how you got x(12-x). can you please explain.
    You have the product P = xy.

    You have the condition x + y = 12. From this condition, it follows that y = 12 - x. So let y = 12 - x in P = xy.

    Then you have P = x (12 - x).

    Then you want to find the maximum value of P. Note that the graph of P = x (12 - x) is a parabola and the maximum value occurs at its turning point ...... (although you could also use calculus to get the coordinates of the turning point).
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: July 26th 2010, 05:24 PM
  2. Differentiation and partial differentiation
    Posted in the Calculus Forum
    Replies: 2
    Last Post: May 30th 2010, 10:16 PM
  3. Differentiation
    Posted in the Calculus Forum
    Replies: 1
    Last Post: February 4th 2010, 10:45 AM
  4. Differentiation Help
    Posted in the Calculus Forum
    Replies: 1
    Last Post: January 25th 2010, 06:20 PM
  5. Differentiation and Implicit Differentiation
    Posted in the Calculus Forum
    Replies: 1
    Last Post: February 6th 2009, 04:07 AM

Search Tags


/mathhelpforum @mathhelpforum