Given the real function of a real variable $f ( x ) = x - \frac { 4 } { ( x - 1 ) ^ { 2 } }$, it is requested:
a) ( 0.75 points) Find the domain of definition of $f ( x )$ and determine, if they exist, the equations of the asymptotes of its graph.
b) (1 point) Determine the relative extrema of the function, as well as its intervals of increase and decrease.
c) ( 0.75 points) Calculate the equation of a tangent line to the graph of $f ( x )$ that is parallel to the line with equation $9 x - 8 y = 6$.

Consider the real coefficient polynomial $f ( x ) = x ^ { 4 } - 4 x ^ { 3 } - 2 x ^ { 2 } + a x + b$. It is known that the equation $f ( x ) = 0$ has a complex root $1 + 2 i$ (where $i = \sqrt { - 1 }$). Select the correct options.
(1) $1 - 2i$ is also a root of $f ( x ) = 0$
(2) Both $a$ and $b$ are positive numbers
(3) $f ^ { \prime } ( 2.1 ) < 0$
(4) The function $y = f ( x )$ has a local minimum at $x = 1$
(5) The $x$-coordinates of all inflection points of the graph $y = f ( x )$ are greater than 0

Determine the number of stationary points on the curve with equation
$$y = 3 x ^ { 4 } + 4 x ^ { 3 } + 6 x ^ { 2 } - 5$$
A 0
B 1
C 2
D 3
E 4