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Math Help - Show that there is only one value of x for which P is stationary..?

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    Show that there is only one value of x for which P is stationary..?

    Sorry if I posted this in the wrong place.



    Two numbers x and y are such that 2x + y = 12.
    The product P is formed by multiplying the first number by the square of the second number so that P = xy

    P = 4x - 48x + 144x



    I worked out the two values of x for which dP/dx = 0
    They are x = 6 and x = 2 (hopefully!)


    Now it says : The values of x and y must both be positive, show that there is only one value of x for which P is stationary.


    How do I do this?
    Please and thank you x
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    Quote Originally Posted by Jayde View Post
    Sorry if I posted this in the wrong place.



    Two numbers x and y are such that 2x + y = 12.
    The product P is formed by multiplying the first number by the square of the second number so that P = xy

    P = 4x - 48x + 144x



    I worked out the two values of x for which dP/dx = 0
    They are x = 6 and x = 2 (hopefully!)


    Now it says : The values of x and y must both be positive, show that there is only one value of x for which P is stationary.


    How do I do this?
    Please and thank you x
    x = 2 => y = 8.

    x = 6 => y = 0.

    So there's only one value of x for which x and y are positive (ie. x > 0 and y > 0) ....
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