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.
329 exam-style questions on Edexcel A Level Maths Numerical Methods, covering 10.1 Locating Roots, 10.2 Iteration, 10.3 The Newton-Raphson Method, and 10.4 Applications to Modelling. Each one has a worked solution and a mark scheme showing where the marks go.