Find the coordinates of the minimum point of the curve \(y = \frac { 9 } { 4 } x ^ { 2 } - 12 x + 18\).
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The diagram shows the curves with equations \(y = \frac { 9 } { 4 } x ^ { 2 } - 12 x + 18\) and \(y = 18 - \frac { 3 } { 8 } x ^ { \frac { 5 } { 2 } }\). The curves intersect at the points \(( 0,18 )\) and \(( 4,6 )\).
Find the area of the shaded region.
A point \(P\) is moving along the curve \(y = 18 - \frac { 3 } { 8 } x ^ { \frac { 5 } { 2 } }\) in such a way that the \(x\)-coordinate of \(P\) is increasing at a constant rate of 2 units per second.
Find the rate at which the \(y\)-coordinate of \(P\) is changing when \(x = 4\).
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