f[k_]:=k ((N^2)/2)- k ((s^2)/(2 b (k+b)))

D[f[k],k]//Simplify

kRoots=Solve[D[f[k],k]==0,k]

specificRoots=kRoots/.{s->1,b->1,N->(1/2)}//Simplify

D[f[k],{k,2}]/.{s->1,b->1,N->(1/2)}/.specificRoots