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 March 30th, 2010, 10:14 PM #1 Senior Member   Joined: Jan 2009 From: Russia Posts: 113 Thanks: 0 Extremum of two variables function Please help in finding the extremum of the given function. $f(x)=(3+8x-5y)e^{-21x^2+17xy-3y^2}$ Finding partial derivatives leads to the system of equations $\begin{cases} 8+(3+8x-5y)(-42x+17y)=0 \\ -5+(3+8x-5y)(17x-6y)=0 \end{cases}$ and I'm stuck here. Thank you.
 March 30th, 2010, 10:19 PM #2 Senior Member   Joined: Jan 2009 From: Russia Posts: 113 Thanks: 0 Re: Extremum of two variables function Sorry for triple-post.
March 31st, 2010, 05:22 PM   #3
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Re: Extremum of two variables function

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 Originally Posted by lime Please help in finding the extremum of the given function. $f(x)=(3+8x-5y)e^{-21x^2+17xy-3y^2}$ Finding partial derivatives leads to the system of equations $\begin{cases} 8+(3+8x-5y)(-42x+17y)=0 \\ -5+(3+8x-5y)(17x-6y)=0 \end{cases}$ and I'm stuck here. Thank you.
It looks like you can quickly get (17x-6y)/5=(42x-17y)/8, which gives you a linear relationship between x and y. Then using it in one of your original equations give you a quadratic to solve.

 April 7th, 2010, 11:24 AM #4 Senior Member   Joined: Jan 2009 From: Russia Posts: 113 Thanks: 0 Re: Extremum of two variables function mathman, thank you very much!

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