6
\includegraphics[max width=\textwidth, alt={}, center]{7b39a2ab-305d-43c5-a1e7-9442d6c13886-10_629_620_278_717}
The diagram shows the curve with parametric equations
$$x = 1 + \sqrt { t } , \quad y = ( \ln t + 2 ) ( \ln t - 3 ) ,$$
for \(0 < t < 25\). The curve crosses the \(x\)-axis at the points \(A\) and \(B\) and has a minimum point \(M\).
- Show that \(\frac { \mathrm { dy } } { \mathrm { dx } } = \frac { 4 \mathrm { Int } - 2 } { \sqrt { \mathrm { t } } }\).
- Find the exact gradient of the curve at \(B\).
- Find the exact coordinates of \(M\).