- (i) (a) Show that \(\frac { \mathrm { d } } { \mathrm { d } x } \left( x ^ { \frac { 1 } { 2 } } \ln x \right) = \frac { \ln x } { 2 \sqrt { } x } + \frac { 1 } { \sqrt { } x }\)
The curve with equation \(y = x ^ { \frac { 1 } { 2 } } \ln x , x > 0\) has one turning point at the point \(P\).
(b) Find the exact coordinates of \(P\). Give your answer in its simplest form.
(ii) A curve \(C\) has equation \(y = \frac { x - k } { x + k }\), where \(k\) is a positive constant. Find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\), and show that \(C\) has no turning points.