The function f is given by f: x \to x^4 - 4x + 1.
Show that f(x) = 0 has a root \alpha in the interval (0, 1).
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Practise this questionx_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)…[5 marks]P = 570.[5 marks]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