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Math Help - second order differentiations stationary points problems on maxima and minima.

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    second order differentiations stationary points problems on maxima and minima.

    Two positive quantities, p and q,very in such a way that {p^3}{q}=9.Another quantity z,is defined by z=16p+3q.Find the values of p and q that makes z a minimum.




    help.
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  2. #2
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    you can use Lagrange multipliers - Wikipedia, the free encyclopedia to do this.


     \min_{p,q} L = 16p + 3q  +\lambda \left(p^3q - 9 \right)
    To solve the optimisation problem, differenciate L with respect to p,q and \lambda and set all partial derivatives to zero.
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    Quote Originally Posted by mastermin346 View Post
    Two positive quantities, p and q,very in such a way that {p^3}{q}=9.Another quantity z,is defined by z=16p+3q.Find the values of p and q that makes z a minimum.
    q = \frac{9}{p^3}

    z = 16p + \frac{27}{p^3}

    you've posted this in the precalculus section ... therefore I assume you'll be using technology (rather than calculus) to determine the value of p that minimizes z.
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    lol i cant believe i forgot that...skeeters way is much better
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