A research drone's vertical displacement yyy (in meters) from its starting altitude is modeled by the equation
y=2x2ln(x)−5x,x>0.5y = 2x^2 \ln(x) - 5x, \quad x > 0.5y=2x2ln(x)−5x,x>0.5
where xxx is the horizontal distance in kilometers from the launch point. The drone reaches a minimum altitude at point PPP.
Show, using calculus, that the xxx-coordinate of PPP is a solution of the equation
4xln(x)+2x−5=04x \ln(x) + 2x - 5 = 04xln(x)+2x−5=0
Using the Newton-Raphson method with f(x)=4xln(x)+2x−5f(x) = 4x \ln(x) + 2x - 5f(x)=4xln(x)+2x−5 and a first approximation x1=2x_1 = 2x1=2, find the value of x2x_2x2 and the value of x3x_3x3, giving your answers to 3 decimal places.
Practise Edexcel A Level Maths Numerical Methods with exam-style questions for A Level Maths. 63 questions covering 10.1 Locating Roots, 10.2 Iteration, 10.3 The Newton-Raphson Method, and 10.4 Applications to Modelling, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.