7 The point \(( 4,7 )\) lies on the curve \(y = \mathrm { f } ( x )\) and it is given that \(\mathrm { f } ^ { \prime } ( x ) = 6 x ^ { - \frac { 1 } { 2 } } - 4 x ^ { - \frac { 3 } { 2 } }\).
- A point moves along the curve in such a way that the \(x\)-coordinate is increasing at a constant rate of 0.12 units per second.
Find the rate of increase of the \(y\)-coordinate when \(x = 4\).
- Find the equation of the curve.