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.
125 exam-style questions on OCR A Level Maths 1.9 Numerical Methods (A-level only), covering 1.9.1 Locating roots by sign change (A-level only), 1.9.2 Failure of sign change methods (A-level only), 1.9.3 Simple iterative methods (A-level only), 1.9.4 Newton-Raphson method (A-level only), 1.9.5 Failure of iterative methods (A-level only), 1.9.6 Numerical integration (A-level only), and 1.9.7 Numerical methods in context (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.