Find the absolute maximum and minimum of the function f(x, y) = x^2 + y^2 subject to the constraint x^4 + y^4 = 4096. As usual, ignore unneeded answer blanks, and list points in lexicographic order. Absolute minimum value: 64 attained at ( , ), ( 0 , -8 ), ( , ), ( , ). Absolute maximum value: 90.5 attained at ( 8/(2)^(-1/4) , 8/(2)^(-1/4) ), ( , -8/(2)^(-1/4) ), ( -8/(2)^(-1/4) , 8/(2)^(-1/4) ), ( -8/(2)^(-1/4) , ).
Added by Nicholas R.
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First, we need to find the critical points of the function f(x, y) = x^2 + y^2 subject to the constraint g(x, y) = x^4 + y^4 = 4096. Show more…
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