Mathematics 9709 · AS & A Level · Numerical solution of equations
Numerical solution of equations — practice question
The curve defined by $y = x^2 \cos\left(\tfrac{1}{2}x\right)$ possesses a stationary point at $x = p$ for values of $x$ in the range $0 < x < \pi$.
(a(i))[3]
Show that $p$ meets the equation $\tan\left(\tfrac{1}{2}p\right) = \frac{4}{p}$.
(a(ii))[2]
Use calculations to confirm that $p$ is between $2$ and $2.5$.
(a(iii))[3]
Apply the iterative formula $p_{n+1} = 2\tan^{-1}\left(\frac{4}{p_n}\right)$ to find $p$ correct to 2 decimal places. Record every 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: “Apply the product rule” …