Question 5

The curve $C\,$ has the equation $\ln x$ , $x > 0$ .

Find $dydx\displaystyle \frac{dy}{dx}$

$C\,$ has a stationary point at $P$ . Show that the $x$ -coordinate of $P\,$ lies between 5 and 6.

Show that the $x$ -coordinate of $P\,$ is a solution of $x=151+ln⁡x\displaystyle x = \frac{15}{1 + \ln x}$ .

Use the iteration formula $xn+1=151+ln⁡xn\displaystyle x_{n+1} = \frac{15}{1 + \ln x_n}$ with $x_0 = 5.5$ to find, to 3 decimal places, the values of $x_1$ , $x_2\,$ and $x_3$ .