(a)[4]
Find $\frac{dy}{dx}$ and hence establish that the $x$-coordinate of $P$ satisfies the equation $x = \frac{1}{6} + \frac{1}{2}e^{-2x}$.
(b)[2]
Demonstrate by calculation that the $x$-coordinate of $P$ is between $0.35$ and $0.45$.
(c)[3]
Apply an iterative formula based on the equation in part (a) to determine the $x$-coordinate of $P$ correct to $3$ significant figures. Record the outcome of each iteration to $5$ significant figures.