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” …