Let the nos. be x and y
1st condition. x + y = (1/2)
=> x= (1/2) - y -(1)
To find:
minima for x + y3
from (1) f(y) = (1/2) - y + y3
f'(y) = -1 + 3y2 = 0 (COnd. for Max/ MIN)
=> y =
(1/
[ ]
3)
f''(y) = 6y
By 2nd derivative test f''(y) >0 ie y= (1/root3)
Hence x = (1/2) - y
= (root3 - 1)/ 2root3
Moderation Team
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