I have the following function I want to maximize over I:
(1+k)^2/4-k-0.5(1-k)kI/(I+eps)+0.25(kI/(I+eps))^3-I
With 0<k<=1, 0<eps, 0<I.
With the first order condition I get the following:
k*eps*I+k*eps^2-k^2*eps^2-2(I+eps)^3=0
I had hoped to be able to now write something like I=... as a function of k and eps, but this is not possible.
So I wanted to know for which values of k and eps you'll get that I=0 is maximal and for which values of k and eps I>0 is maximal.
But how?
(1+k)^2/4-k-0.5(1-k)kI/(I+eps)+0.25(kI/(I+eps))^3-I
With 0<k<=1, 0<eps, 0<I.
With the first order condition I get the following:
k*eps*I+k*eps^2-k^2*eps^2-2(I+eps)^3=0
I had hoped to be able to now write something like I=... as a function of k and eps, but this is not possible.
So I wanted to know for which values of k and eps you'll get that I=0 is maximal and for which values of k and eps I>0 is maximal.
But how?