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**calc626** find the critical points of the function f(x,y)= ln(x^2+y^2) inside of the ring-shaped region R= (x,y): 4 <(or = to) x^2+y^2 >(or = to) 16

using lagrange multipliers find the critical points of f(x,y) on the first boundary and then on the second boundary

i got critical points x=0 y= +- sqrt(2) and y=0 x= +- sqrt (2) but i'm not sure

also i found the gradient of each and set them equal with a multiple of lambda so i eventually got..

x= +- sqrt((1-lamdba*y^2)/(lambda))

and y= +- sqrt((1-lamdba*x^2)/(lambda))

but im also not sure if this is right or where to go from there..

thanks for any help!