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In response to
"Math help please"
by
Beaker
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Here's my solution.
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y' = -2x/(x^2+2)^2
y'' = (6x^2-4)/(x^2+2)^3
Solving for y''=0 tells us that y' has local extrema at +/-sqrt(2/3). y'(+sqrt(2/3))<0 and y'(-sqrt(2/3))>0 so x=+sqrt(2/3) must be a minimum and x=-sqrt(2/3) a maximum for y'. Thus y is increasing most rapidly at the latter and decreasing most rapidly at the former.
I think that's right. Haven't done these sorts of problems in ages.
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