The diagram shows part of the curve with equation $$\(y=\frac{5 x}{4 x^{3}+1}\)$$. The shaded region is bounded by the curve and the lines $$\(x=1, x=3\)$$ and $$\(y=0\)$$. Find $$\(\frac{\mathrm{d} y}{\mathrm{~d} x}\)$$ and hence find the $$\(x\)$$-coordinate of the maximum point. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................

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