Question (1 point) Find the absolute maximum and minimum of the function f(x,y) x2 + y2 subject to the constraint x4 + y4 = 16. As usual, ignore unneeded answer blanks, and list points in lexicographic order. Absolute minimum value: = attained at ), ( ), ( ), ( ). Absolute maximum value: attained at . ), ( ), ( ), ( ).
GHTBBB The Asker · Calculus
Transcribed Image Text: (1 point) Find the absolute maximum and minimum of the function f(x,y) x2 + y2 subject to the constraint x4 + y4 = 16. As usual, ignore unneeded answer blanks, and list points in lexicographic order. Absolute minimum value: = attained at ), ( ), ( ), ( ). Absolute maximum value: attained at . ), ( ), ( ), ( ).
More Transcribed Image Text: (1 point) Find the absolute maximum and minimum of the function f(x,y) x2 + y2 subject to the constraint x4 + y4 = 16. As usual, ignore unneeded answer blanks, and list points in lexicographic order. Absolute minimum value: = attained at ), ( ), ( ), ( ). Absolute maximum value: attained at . ), ( ), ( ), ( ).
Community Answer
BUC8H0
f(x,y)=x^(2)+y^(2)Constraint x^(4)+y^(4)=16=>x^(4)+y^(4)-16=0". "Using Langrang multiplien(1) 2x+4lambdax^(3)=0=>2x(1+2lambdax^(2))=0(2) 2y+4lambda y3=0=>2y(1+2lambda^(2))=0(3) x^(4)+y^(4)-16=0By eq (1) x=0,lambda=-(1)/(2x^(2))=>x^(2)=-(1)/(2lambda) put x=0 in constraint, y=+-2(0,+-2)Byeqn@ y=0,lambda=-(1)/(2y^(2))=>y^(2)=(-1)/(2lambda) put y=0 in constraintx=+-2quad(+-2,0)By putting Vallews of x^(2)&y^(2)In ConstraintCS Scanned with CamScanner{:[:.(-(1)/(2lambda))^(2)+(-(1)/(2lambda))^(2)=16],[f(-2","0)=4],[(1)/(4lambda^(2))+(1)/(4lambda^(2))=16],[f(0","-2)=4],[(1)/(2lambda^(2))=16],[f(0","2)=4],[(1)/(lambda^(2))=32],[f ... See the full answer