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.
137 exam-style questions on OCR (MEI) A Level Maths 1.10 Numerical Methods (A-level only), covering 1.10.1 Locate roots by change of sign (A-level only), 1.10.2 When change of sign methods fail (A-level only), 1.10.3 Fixed point iteration (A-level only), 1.10.4 Newton-Raphson method (A-level only), 1.10.5 Convergence of iterations (A-level only), 1.10.6 Trapezium rule (A-level only), 1.10.7 Upper and lower bounds using rectangles (A-level only), and 1.10.8 Numerical methods to solve problems (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.