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    The 2nd one.
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    heh thanks alot fermat, i can understand your 2nd one perfectly, but not your first, can u explain it a bit more if it's not too much trouble ?


    btw is there any 'special' ways of identifying the equations in these type of questions ?
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    (Original post by ronnie)
    heh thanks alot fermat, i can understand your 2nd one perfectly, but not your first, can u explain it a bit more if it's not too much trouble ?


    btw is there any 'special' ways of identifying the equations in these type of questions ?
    Ignore the 1st one - I'll re-do it.
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    i will try my hand at the first one

    take the top point (ie the top point where the rectangle touches the xy=10 graph). this point has coordinates (x,y)
    due to it being symmetrical in x and y axis, one side is 2y, and the other is 2x

    the perimeter of the rectangle is therefore 4x + 4y.
    and the area is (2x)(2y)

    take xy=10. y = 10/x
    perimeter = 4x + 40x-1
    dy/dx = 4 - 40x-2
    dy/dx = 0 (for min/max)
    4 - 40x-2=0
    x²=10
    x=√10
    y=√10

    d²y/dx² = 80x-3
    80/(√10)³>0, so it is a minimum.
    MIN perimeter = 4√10 + 4√10 = 8√10

    Area = (2x)(2y)
    = (2x)(20/x)= 40
    EDIT: Area = 40 = constant, so not min or max
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    Q1)
    Look at the rectangle
    The x- and y-axes are axes of symmetry. therefore P and Q are directly opposite each other on the opposite sides of the origin.

    :. x1 = -x0
    & y1 = -y0

    Perimeter of rectangle is S = 2(x0 + |x1|) + 2(y0 + |y1|)
    (this is just adding the coordinates of P and Q to get the length and height)

    but |x1 | = x0
    and |y1 | = y0

    :. S = 2(2x0) + 2(2y0)
    S = 4x0 + 4y0

    since xy = 10 then
    y0 = 10/x0

    S = 4x0 + 40/x0
    dS/dx0 = 4 - 40/x02 = 0
    :. x02 = 10
    x0 = √10, y0 = √10
    ==============

    S = 4x0 + 4y0
    S = 4√10 + 4√10
    S = 8√10
    =======

    d²S/dx02 = 80/x03, which is +ve for x0 +ve, => S is a min
    ================================ ==============

    Area
    ====
    A = (x0 +|x1|)(y0 + |y1|)
    A = 2x0.2y0
    A = 4x0y0
    A = 40 (xy = 10)
    =====

    i.e. there is no max or min - it is always a constant
    ================================ =======
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    (Original post by Fermat)
    i.e. there is no max or min - it is always a constant
    Ahhh i see. i first did my differentiation of Area wrong (see above) and then did again and got 0. so i agree
 
 
 
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