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

Numerical solution of equations — practice question

The diagram displays the section of the curve $y = x^2 \cos 3x$ for $0 \leq x \leq \frac{\pi}{6}$, together with its maximum point $M$, where $x = a$.
(a)[3]

Show that $a$ fulfils the equation $a = \frac{1}{3} \tan^{-1}\!\left( \frac{2}{3a} \right)$.

(b)[3]

Use an iterative formula based on the equation in (a) to determine $a$ correct to 2 decimal places. Record the result of each iteration to 4 decimal places.

Worked solution & mark scheme

This 6-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