Skip to content
MathsGenie logo
Quick links
Open app

Course home

  1. A Level
  3. Maths WJEC
  5. Question bank

3.8.3 Numerical Methods (A-level only)

MediumHard
12345678910111213141516171819
Question 17

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]

3.8.3 Numerical Methods (A-level only) Questions

  1. A Level
  2. /Maths
  3. /3.8.3 Numerical Methods (A-level only)