9709 P13 - Jun 2016 - Q3
1379
A curve is such that \(\frac{dy}{dx} = 6x^2 + \frac{k}{x^3}\) and passes through the point \(P(1, 9)\). The gradient of the curve at \(P\) is 2.
(i) Find the value of the constant \(k\).
(ii) Find the equation of the curve.
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