f(x)=ln(2x+1)+x2−6x>−0.5f(x) = \ln(2x + 1) + x^2 - 6 \quad x > -0.5f(x)=ln(2x+1)+x2−6x>−0.5
f′(x)=22x+1+2xf'(x) = \dfrac{2}{2x+1} + 2xf′(x)=2x+12+2x
Using x0=2.0x_0 = 2.0x0=2.0 as a first approximation, apply the Newton-Raphson procedure to find a second approximation, giving your answer to 3 decimal places.
321 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.