6.
$$f ( x ) = \frac { ( 2 x + 1 ) ( x + 4 ) } { \sqrt { } x } , \quad x > 0$$
- Show that \(\mathrm { f } ( x )\) can be written in the form \(P x ^ { \frac { 3 } { 2 } } + Q x ^ { \frac { 1 } { 2 } } + R x ^ { - \frac { 1 } { 2 } }\), stating the values of the constants \(P , Q\) and \(R\).
- Find f \({ } ^ { \prime } ( x )\).
- Show that the tangent to the curve with equation \(y = \mathrm { f } ( x )\) at the point where \(x = 1\) is parallel to the line with equation \(2 y = 11 x + 3\).
(3)
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