
Maxima proof
Hello!
I have a question I'm struggling with, my last question was answered so helpfully I thought I'd try my others out here! Especially since my exam is in less than 3 hours!
Its a 'Two variable function Extrema' question
Q: The gravitational attraction at the point (x,y)=(1/x)+(4/y)+(9/(4xy))
Prove that G(x,y) has a maximum value of 9
These type of questions always stump me, sorry.
Thanks for any aid

Stump?
I can see why it stumped you. First, how did the exam go? Second, this function has no maximum (or minimum), local or absolute. (Surprised)
$\displaystyle G(x,y)=\frac1x+\frac4y+\frac9{4xy}$
Consider: $\displaystyle \lim_{x+y\to 4}G(x,y)=\pm\infty$ and $\displaystyle \lim_{x,y\to\infty}G(x,y)=0$ because of the $\displaystyle \frac9{4xy}$ term.
For traditional proof, $\displaystyle \bigtriangledown G=\vec{0}$ has no solution.