3. (i) Find the co-ordinates of the turning points of

$$f ( x ) = e ^ { x } \left( 2 x ^ { 2 } - x - 1 \right)$$

(ii) Sketch the graph of $y = f ( x )$ on the axes below for the range $- 4 \leqslant x \leqslant 2$.\\
(iii) Now consider

$$g ( x ) = \left\{ \begin{array} { c c } 
e ^ { x } \left( 2 x ^ { 2 } - x - 1 \right) & \text { if } x < 1 ; \\
\sin ( x - 1 ) & \text { if } x \geqslant 1 .
\end{array} \right.$$

Determine, with explanations, the maximum and minimum values of $g ( x )$ as $x$ varies over the real numbers.\\
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