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1.12 I: Numerical methods (A-level only)

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Question 68

A research drone's vertical displacement yyy (in meters) from its starting altitude is modeled by the equation

y=2x2ln⁡(x)−5x,x>0.5 y = 2x^2 \ln(x) - 5x, \quad x > 0.5 y=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.

a.

Show, using calculus, that the xxx-coordinate of PPP is a solution of the equation

4xln⁡(x)+2x−5=0 4x \ln(x) + 2x - 5 = 0 4xln(x)+2x−5=0
[3]
b.

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.

[4]

1.12 I: Numerical methods (A-level only) Questions

  1. A Level
  2. /Maths
  3. /1.12 I: Numerical methods (A-level only)

Practise AQA A Level Maths 1.12 I: Numerical methods (A-level only) with exam-style questions for A Level Maths. 107 questions covering 1.12.1 Locating roots by change of sign (A-level only), 1.12.2 Iterative methods and Newton-Raphson (A-level only), 1.12.3 Numerical integration (A-level only), and 1.12.4 Numerical methods in context (A-level only), matched to the AQA A Level Maths (7357) 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.

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