Find the absolute maximum and minimum of the function f(x,y)=x^2+y^2 subject to

Question

Find the absolute maximum and minimum of the function f(x,y)=x^2+y^2 subject to the constraint x^4+y^4=10000 . List points in an order so that the points with smallest x-values come first with smaller y-values first if the x-values are the same. For example, (-3,1), (-3,4), (2,5), (4,-1), (4,0) is a proper ordering..... Absolute minimum value:(_____) attained at (_,_) and (_,_). Absolute maximum value: (_____) attained at (_, _) and (_, _) and (_, _) and (_, _) if someone show me a steps i appreciated it

Explanation / Answer

f(x,y)=x^2+y^2 = x^2 +[ 10^4-x^4]^1/2... f'(x,y) = 2x -4x^3[ 10^4-x^4]^(-1/2).... f'(x,y) =0 ... 2x -4x^3[ 10^4-x^4]^(-1/2) = 0 .... solve for x ....

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