For the curve $y = e^{-2x} \ln(x - 1)$, a stationary point occurs when $x = p$.
(i)[3]
Show that $p$ satisfies $x = 1 + \exp\left( \frac{1}{2(x - 1)} \right)$, with $\exp(x)$ meaning $e^x$.
(ii)[2]
Verify by calculation that $p$ lies between $2.2$ and $2.6$.
(iii)[3]
Use an iterative formula based on the equation in part (i) to find $p$ correct to 2 decimal places. Record each iteration to 4 decimal places.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Use the product rule correctly” …
- Full mark scheme, point by point
- Step-by-step worked solution
- Write your answer & get it marked instantly by AI