Problem #1147
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1147
It is given that a curve has equation \(y = k(3x-k)^{-1} + 3x\), where \(k\) is a constant.
(a) 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 \(f(x) = 4(3x-4)^{-1} + 3x\) for \(x \geq \frac{3}{2}\).
(b) Find the value of \(a\) and determine the nature of the stationary value.
(c) The function \(g\) is defined by \(g(x) = -(3x+1)^{-1} + 3x\) for \(x \geq 0\).
Determine, making your reasoning clear, whether \(g\) is an increasing function, a decreasing function or neither.
