A curve has equation y=ln(5−4x)+x2−2xy = \ln(5 - 4x) + x^2 - 2xy=ln(5−4x)+x2−2x. Given that the curve intersects the xxx-axis at exactly one point.
Show that the xxx-coordinate of this point lies between 0 and 1 and hence use the Newton-Raphson method, with initial value x0=1x_0 = 1x0=1, to find the xxx-coordinate of the point where the curve intersects the xxx-axis, giving your answer correct to 5 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.