(i)[4]
Find an expression for $\frac{dy}{dx}$ and determine the gradient of the curve at the point where it meets the $x$-axis.
(ii)[2]
Show that the $x$-coordinate of point $M$ satisfies the equation $x = \sqrt{0.6x + 4x^{-1}}$.
(iii)[3]
Use an iterative formula based on the equation in part (ii) to determine the $x$-coordinate of $M$ correct to 3 significant figures. Record the result of each iteration to 5 significant figures.