AP EAMCET20227 Jul 2022Evening ShiftMathematicsApplication of DerivativesActual

If x+y=k, x>0, y>0 , then x^2+y^2 is minimum, if

Options

Ax>y
Bx < y
Cx=y
Dx=2 y

Correct answer

C. x=y

Step-by-step solution

gathered x+y=k y=k-x, x>0, y>0 gathered Consider aligned & A=x^2+y^2=x^2+(k-x)^2=2 x^2-2 k x+k^2 & d A d x =4 x-2 k=0 x= k 2 & d^2 A d x^2 =4>0 aligned At x=y= k 2 , we have Minimum vale of x^2+y^2 .

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