题目

Problem

$f(x) = x^3 - \dfrac{10}{x} + \dfrac{4}{x^2}$ , $x > 0$

(a) Show that the equation $f(x) = 0$ has a root $\alpha$ in the interval $[1.4, 1.5]$

(2)

(b) Determine $f'(x)$ .

(3)

(c) Using $x_0 = 1.4$ as a first approximation to $\alpha$ , apply the Newton-Raphson procedure once to $f(x)$ to calculate a second approximation to $\alpha$ , giving your answer to 3 decimal places.

(2)

题目中文翻译

$f(x) = x^3 - \dfrac{10}{x} + \dfrac{4}{x^2}$ ， $x > 0$

(a) 证明方程 $f(x) = 0$ 在区间 $[1.4, 1.5]$ 内有一个根 $\alpha$ 。

(b) 求 $f'(x)$ 。

IAL 2020 May FP1 Q1

题目

解答