Consider the family of functions $f ( x ) = \frac { 1 } { x ^ { 2 } - 2 x + k }$, where $k$ is a constant.
(a) Find the value of $k$, for $k > 0$, such that the slope of the line tangent to the graph of $f$ at $x = 0$ equals 6.
(b) For $k = - 8$, find the value of $\int _ { 0 } ^ { 1 } f ( x ) \, dx$.
(c) For $k = 1$, find the value of $\int _ { 0 } ^ { 2 } f ( x ) \, dx$ or show that it diverges.