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\includegraphics[max width=\textwidth, alt={}, center]{6295873e-7db4-4e7e-8dcd-912ad9c41675-10_643_414_260_863}
The diagram shows the curve with equation
$$y = 3 x ^ { 2 } \ln \left( \frac { 1 } { 6 } x \right) .$$
The curve crosses the \(x\)-axis at the point \(P\) and has a minimum point \(M\).
- Find the gradient of the curve at the point \(P\).
- Find the exact coordinates of the point \(M\).