f(x)=3sin(x)−12x2\displaystyle f(x) = 3\sin(x) - \frac{1}{2}x^2f(x)=3sin(x)−21x2
Show that y=f(x)y = f(x)y=f(x) has a stationary point in the interval [1.1,1.2][1.1, 1.2][1.1,1.2]
Starting with x0=1.15x_0 = 1.15x0=1.15, apply the Newton-Raphson procedure twice to find an approximation for the x x\,x coordinate of the stationary point in the interval [1.1,1.2][1.1, 1.2][1.1,1.2]. Give your answer to 3 decimal places.
Practise AQA A Level Maths 1.12 I: Numerical methods (A-level only) with exam-style questions for A Level Maths. 107 questions covering 1.12.1 Locating roots by change of sign (A-level only), 1.12.2 Iterative methods and Newton-Raphson (A-level only), 1.12.3 Numerical integration (A-level only), and 1.12.4 Numerical methods in context (A-level only), matched to the AQA A Level Maths (7357) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
