I presume that the formula is:

P = 0.1g + 1000/(1 + g)

PLEASE use parenthesis!!

To find the minimum we take the first derivative:

dP/dg = 0.1 + 1000*(-1)/(1 + g)^2

then set it equal to 0:

0.1 + 1000*(-1)/(1 + g)^2 = 0

0.1 = 1000/(1 + g)^2

0.1(1 + g)^2 = 1000

(1 + g)^2 = 1000/0.1 = 10000

1 + g = 100 <-- Technically (+/-)100, but since g can't be negative...

g = 100 - 1 = 99

I'll let you prove that this value of g provides a minimum.

-Dan