5 Differentiate \(4 x ^ { 2 } + \frac { 1 } { x }\) and hence find the \(x\)-coordinate of the stationary point of the curve \(y = 4 x ^ { 2 } + \frac { 1 } { x }\).
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{bba82ee6-90b2-4f03-9bb9-0371ff711a09-3_639_1027_302_542}
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\caption{Fig. 11}
\end{figure}
The equation of the curve shown in Fig. 11 is \(y = x ^ { 3 } - 6 x + 2\).
- Find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\).
- Find, in exact form, the range of values of \(x\) for which \(x ^ { 3 } - 6 x + 2\) is a decreasing function.
- Find the equation of the tangent to the curve at the point \(( - 1,7 )\).
Find also the coordinates of the point where this tangent crosses the curve again.