Consider the differential equation $\frac { d y } { d x } = e ^ { y } \left( 3 x ^ { 2 } - 6 x \right)$. Let $y = f ( x )$ be the particular solution to the differential equation that passes through $( 1, 0 )$.
(a) Write an equation for the line tangent to the graph of $f$ at the point $( 1, 0 )$. Use the tangent line to approximate $f ( 1.2 )$.
(b) Find $y = f ( x )$, the particular solution to the differential equation that passes through $( 1, 0 )$.