Area!!!

first find the points where the two curves are equal...

so a²-ax=x²+2ax+3a²

so 0=x²+3ax+2a²

Hence, x=-a and x=-2a are teh roots

now we need to find the integral.. between -2a and -a

f(x)-g(x) = x²+3ax+2a²1+a⁴

INtegral of this will be x³/3+3/2ax²+2a²x1+a⁴

applying limits from -2a to -a we get

(-8a³/3+3x2a.a²+2a²(-2a))-(-a³/3+3/2aa²+2a²a)1+a⁴

(1/6a³)1+a⁴

=(1/6)a+a^-3

maximizing the above is same as minimizing a+a^-3
derivative is 1-3a^-4

double derivative is +ve...
a=3^1/4

Make sure i have not made any calculation mistake.. bcos there were a few of those involved...

:)