Mathematics 9709 · AS & A Level · Numerical solution of equations

Numerical solution of equations — practice question

For $x > 0$, define $f(x) = \frac{e^{2x} + 1}{e^{2x} - 1}$.
(a)[2]

The equation $x = f(x)$ has a single root, written as $a$. Confirm by calculation that $a$ is between $1$ and $1.5$.

(b)[3]

Using an iterative formula derived from the equation in part (a), determine $a$ correct to $2$ decimal places. Give each iterate to $4$ decimal places.

(c)[6]

Find $f'(x)$. Hence determine the exact value of $x$ for which $f'(x) = -8$.

Worked solution & mark scheme

This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: Evaluate the relevant expression when $x=1$ and when $x=1.5$

  • Full mark scheme, point by point
  • Step-by-step worked solution
  • Write your answer & get it marked instantly by AI