A curve $y = f\left( x \right)$ has a stationary point at $P\left( {3,{\text{ }} - 10} \right)$. It is given that $f\prime \left( x \right) = 2{x^2} + kx - 12$, where $k$ is a constant.
a) Show that $k = - 2$ and hence find the x-coordinate of the other stationary point, $Q$.
b) Find $f''\left( x \right)$ and determine the nature of each of the stationary points $P$ and $Q$.
c) Find $f\left( x \right)$.
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