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\includegraphics[max width=\textwidth, alt={}, center]{388d7076-636c-417d-84cb-e6e2a3e9a6a0-08_451_1086_260_525}
The diagram shows the curve with equation
$$y = ( \ln x ) ^ { 2 } - 2 \ln x$$
The curve crosses the \(x\)-axis at the points \(A\) and \(B\), and has a minimum point \(M\).
- Find the exact value of the gradient of the curve at each of the points \(A\) and \(B\).
- Find the exact \(x\)-coordinate of \(M\).