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1.12 I: Numerical methods (A-level only)

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Question 17

f(x)=2x3−6x+3xx>0f(x) = 2x^3 - 6x + 3\sqrt{x} \quad x > 0f(x)=2x3−6x+3x​x>0

a.

Show that f(x)=0f(x) = 0f(x)=0 has a root in the interval [1.2,1.3][1.2, 1.3][1.2,1.3]

[2]
b.

Find f′(x)f'(x)f′(x)

[3]
c.

Starting with x0=1.25x_0 = 1.25x0​=1.25, apply the Newton-Raphson procedure once to find an approximate solution to the equation f(x)=0f(x) = 0f(x)=0 giving your answer to 3 decimal places.

[3]
Markscheme

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

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

125 exam-style questions on AQA A Level Maths 1.12 I: Numerical methods (A-level only), 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). Each one has a worked solution and a mark scheme showing where the marks go.

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