Figure 1 below shows part of the curve y=2xsinxy = 2x\sin xy=2xsinx, where x x\,x is measured in radians. The maximum point on the curve is PPP.
Show that the xxx-coordinate of P P\,P satisfies the equation
tanx+x=0\tan x + x = 0tanx+x=0
Use the Newton-Raphson method, with a suitable initial value, to find the xxx-coordinate of PPP, giving your answer correct to four decimal places. Show the result of each iteration.
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.