I have to find the number of maximum local points (n) and asymptotes (k).

From my work here i found out that n = 1 and k = 1. Is this correct?

Ah, i forgot to type there that g(x) = 0 has the unique solution x = -1, and in the table it's g'(x) g(x) not f'(x) f(x)

Oh, there's one more thing: i REALLY want to know if there's a faster method of doing this, maybe without going through all these steps...