Show that \(\dfrac{\mathrm{d}y}{\mathrm{d}x}=\dfrac{3\pi^2(1-\pi)}{16}\) when \(x=\dfrac\pi4\).[5]
Given that \(y\) is decreasing at a rate of 3 units per second, find the rate of change of \(x\), in terms of \(\pi\), at the instant when \(x=\dfrac\pi4\).[2]
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Answer:(a) \(\dfrac{3\pi^2(1-\pi)}{16}\) (shown). (b) \(\dfrac{16}{\pi^2(\pi-1)}\) units per second, increasing.