11 It is given that a curve has equation \(y = k ( 3 x - k ) ^ { - 1 } + 3 x\), where \(k\) is a constant.
- Find, in terms of \(k\), the values of \(x\) at which there is a stationary point.
The function f has a stationary value at \(x = a\) and is defined by
$$f ( x ) = 4 ( 3 x - 4 ) ^ { - 1 } + 3 x \quad \text { for } x \geqslant \frac { 3 } { 2 }$$ - Find the value of \(a\) and determine the nature of the stationary value.
- The function g is defined by \(\mathrm { g } ( x ) = - ( 3 x + 1 ) ^ { - 1 } + 3 x\) for \(x \geqslant 0\).
Determine, making your reasoning clear, whether \(g\) is an increasing function, a decreasing function or neither.
If you use the following lined page to complete the answer(s) to any question(s), the question number(s) must be clearly shown.