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The diagram shows the curve with equation \(y = 9 \left( x ^ { - \frac { 1 } { 2 } } - 4 x ^ { - \frac { 3 } { 2 } } \right)\). The curve crosses the \(x\)-axis at the point \(A\).
- Find the \(x\)-coordinate of \(A\).
- Find the equation of the tangent to the curve at \(A\).
- Find the \(x\)-coordinate of the maximum point of the curve.
- Find the area of the region bounded by the curve, the \(x\)-axis and the line \(x = 9\).
If you use the following lined page to complete the answer(s) to any question(s), the question number(s) must be clearly shown.