Two variables, \(x\) and \(y\), are related by the equation \(y=\dfrac34\left(\dfrac{x}{12}-1\right)^6\). Given that both \(x\) and \(y\) vary with time, find the value of \(y\) when the rate of change of \(y\) is 12 times the rate of change of \(x\).[4]
The function \(\mathrm{f}\) is given by \(\mathrm{f}(x)=\dfrac{\mathrm e^{2x}}{1-x}\) for \(x>1\). Show that \(\mathrm{f}\) is a decreasing function.[3]
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Answer:(a) \(y=48\). (b) False as printed; decreasing for \(x>\dfrac32\), the school key's corrected domain.