Quelpr
5 marksRoots of Equations

CAPE Pure Mathematics Unit 2 · May/June 2007 · Paper 2 · Question 4(a)(ii)

The function f is given by f: x \to x^4 - 4x + 1.

If x_1 is a first approximation to \alpha of f(x) = 0 in (0, 1), show that the Newton-Raphson method gives a second approximation x_2 in (0, 1) satisfying x_2 = \frac{3x_1^4 - 1}{4(x_1^3 - 1)}.

The mark scheme is shown once you've answered.

Practise this question

Other parts of this question

  1. 4(a)(i)Show that f(x) = 0 has a root \alpha in the interval (0, 1).[4 marks]
  2. 4(b)(i)Show that P = 570.[5 marks]
  3. 4(b)(ii)Find, in terms of n, 1 \le n \le 12, an expression for the remaining debt on the loan after John has paid the n-th instalment.[6 marks]

More practice: the rest of this paper · more Roots of Equations questions · all CAPE Pure Mathematics Unit 2 past papers