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0606 P13 - Nov 2017 - Q8 - 8 marks
8644

It is given that \(y=(x-4)(3x-1)^{\frac53}\).

(i) Show that \(\dfrac{dy}{dx}=(3x-1)^{\frac23}(Ax+B)\), where \(A\) and \(B\) are constants to be found.

(ii) Hence find, in terms of \(h\), the approximate change in \(y\) when \(x\) increases from \(3\) to \(3+h\), where \(h\) is small.

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