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1.10.4 Newton-Raphson method (A-level only)

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Question 16

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

2x^2 \ln(x) - 5x, \quad x > 0.5

where $x$ is the horizontal distance in kilometers from the launch point. The drone reaches a minimum altitude at point $P$ .

Show, using calculus, that the $x$ -coordinate of $P$ is a solution of the equation

\ln(x) + 2x - 5 = 0

[3]

Using the Newton-Raphson method with $\ln(x) + 2x - 5$ and a first approximation $x_1 = 2$ , find the value of $x_2$ and the value of $x_3$ , giving your answers to 3 decimal places.

[4]

Markscheme

1.10.4 Newton-Raphson method (A-level only) Questions

A Level
Maths
1.10.4 Newton-Raphson method (A-level only)

20 exam-style questions on OCR (MEI) A Level Maths 1.10.4 Newton-Raphson method (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

1.10.4 Newton-Raphson method (A-level only)

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1.10.4 Newton-Raphson method (A-level only)

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Question 16

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

2x^2 \ln(x) - 5x, \quad x > 0.5

where $x$ is the horizontal distance in kilometers from the launch point. The drone reaches a minimum altitude at point $P$ .

Show, using calculus, that the $x$ -coordinate of $P$ is a solution of the equation

\ln(x) + 2x - 5 = 0

[3]

Using the Newton-Raphson method with $\ln(x) + 2x - 5$ and a first approximation $x_1 = 2$ , find the value of $x_2$ and the value of $x_3$ , giving your answers to 3 decimal places.

[4]

Markscheme

1.10.4 Newton-Raphson method (A-level only) Questions

A Level
Maths
1.10.4 Newton-Raphson method (A-level only)

20 exam-style questions on OCR (MEI) A Level Maths 1.10.4 Newton-Raphson method (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.