Cot ^-1 (x^2- x^4) horizontal asymptote

cot ^-1 (x^2- x^4) horizontal asymptote

y = cot ^-1 (x^2- x^4)
cot y = x^2 - x^4
Differentiate with respect to x,
-csc y y' = 2x - 4x^3
y' = 0 => 2x(1 - 2x^2) = 0
x = 0 => y = pi/2
1 - 2x^2 = 0 => x = +/-sqrt(2)/2 => y = cot^-1(1/2 - 1/4) = cot^-1(1/2)
Answer: y = pi/2, and y = cot^-1(1/2)