6. Consider the differential equation given by $\frac { d y } { d x } = x ( y - 1 ) ^ { 2 }$.\\
(a) On the axes provided, sketch a slope field for the given differential equation at the eleven points indicated.\\
(Note: Use the axes provided in the pink test booklet.)\\
\includegraphics[max width=\textwidth, alt={}, center]{fad49542-c73b-43b8-bcac-565b0480224d-5_654_1176_431_472}\\
(b) Use the slope field for the given differential equation to explain why a solution could not have the graph shown below.\\
\includegraphics[max width=\textwidth, alt={}, center]{fad49542-c73b-43b8-bcac-565b0480224d-5_656_1174_1248_472}\\
(c) Find the particular solution $y = f ( x )$ to the given differential equation with the initial condition $f ( 0 ) = - 1$.\\
(d) Find the range of the solution found in part (c).

\section*{END OF EXAMINATION}
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