OK, I have a question about this problem. I'm solving for the absolute maximum value for a function of two variables. I THINK i know what i'm doing, but feel free to rip into me and tell me that I'm clueless(adsbygoogle = window.adsbygoogle || []).push({});

The function is

[tex]f(x , y) = \frac{-2x}{x^2+y^2+1}[/tex]

on the boundary of [tex] \left\{\begin{array}{r} 0 \leq x \leq 2\\ \|y\| \leq x \end{array}\right.[/tex]

Anywho, I've computed the partials easily enough

[tex]F_x = \frac{2(x^2-y^2-1)}{(x^2+y^2+1)^2}[/tex]

[tex]F_y = \frac{4xy}{(x^2+y^2+1)^2}[/tex]

So, i set each of those equal to zero to determine when there will be a critical point. So they will occur when:

[tex] \left\{\begin{array}{r} x^2-y^2-1=0\\xy=0 \end{array}\right.[/tex]

So right of the bat I know that (0,0) and (1,0) are critical points. But what i'm not sure of is whether or not that's all of them. I'm pretty sure that it is, but I'm having a bit of trouble convincing myself why non-integer values of x between 0 and 2 won't work.

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# Homework Help: Multivar Max Value

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