Question

if x^2+y^2=4 find max of x^3+y^3/x+y​

Answer 1

Let t=xy

substituting x from (i)

t=(4+2y)y

t=2y

2

+4y

At minimum value of t

dy

dt

=0

dy

d

(2y

2

+4y)=0

⇒4y+4=0

⇒y=−1

⇒t=(4+2y)y

⇒t=(4−2)(−1)=−2

So minimum value is −2