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Math Help - word problem using implicit differentiation

  1. #1
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    Exclamation word problem using implicit differentiation

    Hi everyone, I was wondering if someone could help me with this problem:

    At a certain factory, output Q is related to inputs u and v by the equation:
    Q=3u^2 + ((2u+3v)/(u+v)^2)

    If the current levels of input are u=10 and v=25, use calculus to estimate the change in input v that should be made to offset a decrease of 0.7 unit in input u so that output will be maintained at its current level.
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  2. #2
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    Quote Originally Posted by steverunner View Post
    Hi everyone, I was wondering if someone could help me with this problem:

    At a certain factory, output Q is related to inputs u and v by the equation:
    Q=3u^2 + ((2u+3v)/(u+v)^2)

    If the current levels of input are u=10 and v=25, use calculus to estimate the change in input v that should be made to offset a decrease of 0.7 unit in input u so that output will be maintained at its current level.
    I do not think you need implicit differentation. you may want to use differentials

    \Delta Q \approx dQ=\frac{\partial Q}{\partial u}\Delta u +\frac{\partial Q}{\partial v}\Delta v

    This should get you started.
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  3. #3
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    thanks, could you possibly solve the problem for me, so I can see how to do it?
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