Yea. I got the same.
P = L[1]/x^2+L[2]/(m-x)^2
dP/dx = -2*L[1]/x^3+2*L[2]/(m-x)^3
Then by making this equal to zero,
x = m*L[1]^(1/3)/(L[1]^(1/3)+L[2]^(1/3))
d^2*P/dx^2 = 6*L[1]/x^4+6*L[2]/(m-x)^4
As the denominators are to the power of 4, they are always +, and as L1 and L2 are...