# word problem using implicit differentiation

• Feb 16th 2010, 10:09 AM
steverunner
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.
• Feb 16th 2010, 10:35 AM
TheEmptySet
Quote:

Originally Posted by steverunner
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

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

This should get you started.
• Feb 16th 2010, 10:41 AM
steverunner
thanks, could you possibly solve the problem for me, so I can see how to do it?