A curve has equation $$\(y=x^{3} \mathrm{e}^{0.2 x}\)$$ where $$\(x \geqslant 0\)$$. At the point $$\(P\)$$ on the curve, the gradient of the curve is 15 . Use the equation in part (a) to show by calculation that the $$\(x\)$$-coordinate of $$\(P\)$$ lies between $$\(1.7\)  and \(1.8\)$$ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................

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