(a)[2]
Derive an expression for $\frac{dy}{dx}$.
(b)[2]
Prove that the $x$-coordinate of $M$ obeys $x = \frac{x + 3}{\ln(2x + 1)} - 0.5$.
(c)[2]
Use calculations to demonstrate that the $x$-coordinate of $M$ is between $2.5$ and $3.0$.
(d)[3]
Apply an iterative formula derived from the equation in part (b) to determine the $x$-coordinate of $M$ correct to $4$ significant figures. State each iteration result to $6$ significant figures.