
Differential Equations Ordinary and Partial Differential Equations Math Forum 
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November 10th, 2016, 06:32 AM  #1 
Member Joined: Dec 2015 From: England Posts: 30 Thanks: 0  Please help
I have spent the last few days try to work out how to do this question and I am not getting anywhere.

November 10th, 2016, 07:01 AM  #2 
Senior Member Joined: Sep 2015 From: USA Posts: 1,977 Thanks: 1026 
differentiate $I(v,T)$ with respect to v set the derivative equal to 0 and solve for v treating T as a constant you should end up with the equation they ask for the problem states you don't have to bother with the second derivative check to ensure the critical point found above is in fact a maxima so you don't need to do that. 
November 11th, 2016, 12:34 AM  #3 
Member Joined: Dec 2015 From: England Posts: 30 Thanks: 0 
Would I use the quotient rule in order to differentiate it?

November 11th, 2016, 07:50 AM  #4 
Global Moderator Joined: Dec 2006 Posts: 19,059 Thanks: 1618 
Yes, that should work.
