<p>its a max/min porblemo</p>
<p>find all ordered pairs (x,y) such that xy=9 and rad(x^2+y^2) is a minimum.</p>
<p>xy=9, thus x=9/y</p>
<p>rad(x^2+y^2)=rad(81*y^-2+y^2)</p>
<p>Minimizing this quantity is equivalent to minimizing the expression under the radicals.</p>
<p>So, take first derivative and set to zero (to find critical points):</p>
<p>-162*y^-3+2y=0
-81+y^4=0</p>
<p>Thus, y=+-3, and same thing for x.</p>
<p>do u thing this would show up on the AP Cal exam?</p>
<p>something like this... I wouldnt doubt it</p>
<p>possible im reviewing everything and this stumped me. these problems just look confusing i got a whole list that i just stare at and dont know how to solve</p>
<p>Sure - lets be honest, this isn't exactly a hard problem. You can actually do it without calc entirely.</p>
<p>ive got more if anyone wants to try another</p>