# how should we choose two numbers each greater than or equal to -2, whose sum is ½ so that the sum of the first and the cube of the second is minimum?

Arun Kumar IIT Delhi
8 years ago
Hi

$\\a,b \geq -2 \\a+b={-1 \over 2}=>{db \over da}=-1 \\a+b^3=c \\=>1+3b^2*{db \over da}=0 \\=>{db \over da}={-1 \over 3b^2}=-1 \\=>b^2={1 \over 3} b=\pm {1 \over \sqrt3}$

you can find a.

Thanks & Regards, Arun Kumar, Btech,IIT Delhi, Askiitians Faculty