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\includegraphics[max width=\textwidth, alt={}, center]{4d8fcc3d-a2da-4d98-8500-075d10847be3-2_636_947_1738_598}
The diagram shows the curve \(y = 7 \sqrt { } x\) and the line \(y = 6 x + k\), where \(k\) is a constant. The curve and the line intersect at the points \(A\) and \(B\).
- For the case where \(k = 2\), find the \(x\)-coordinates of \(A\) and \(B\).
- Find the value of \(k\) for which \(y = 6 x + k\) is a tangent to the curve \(y = 7 \sqrt { } x\).