1 Pure Mathematics
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Question 460
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.
a.[3]
Show that the xxx-coordinate of P P\,P satisfies the equation
tanx+x=0\tan x + x = 0tanx+x=0
b.[4]
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.