| Exam Board | Edexcel |
|---|---|
| Module | F1 (Further Pure Mathematics 1) |
| Year | 2020 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Topic | Newton-Raphson method |
| Type | Newton-Raphson with complex derivative required |
| Difficulty | Standard +0.8 This Further Pure 1 question requires simplifying a complex rational expression involving fractional powers, applying quotient rule differentiation carefully, then executing Newton-Raphson. The algebraic manipulation of f(x) and finding f'(x) with terms like x^(-2) and x^(1/2) is non-trivial and error-prone, elevating this above a standard Newton-Raphson application which would rate around 0.0. |
| Spec | 1.07i Differentiate x^n: for rational n and sums1.09a Sign change methods: locate roots1.09d Newton-Raphson method |
1.
$$f ( x ) = x ^ { 3 } - \frac { 10 \sqrt { x } - 4 x } { x ^ { 2 } } \quad x > 0$$
\begin{enumerate}[label=(\alph*)]
\item Show that the equation $\mathrm { f } ( x ) = 0$ has a root $\alpha$ in the interval[1.4,1.5]
\item Determine $\mathrm { f } ^ { \prime } ( x )$ .
\item Using $x _ { 0 } = 1.4$ as a first approximation to $\alpha$ ,apply the Newton-Raphson procedure once to $\mathrm { f } ( x )$ to calculate a second approximation to $\alpha$ ,giving your answer to 3 decimal places.\\
$f ( x ) = x ^ { 3 } - \frac { 10 \sqrt { x } - 4 x } { x ^ { 2 } } \quad x > 0$\\
(a)Show that the equation $\mathrm { f } ( x ) = 0$ has a root $\alpha$ in the interval[1.4,1.5]\\
(b)Determine $\mathrm { f } ^ { \prime } ( x )$ .
\end{enumerate}
\hfill \mbox{\textit{Edexcel F1 2020 Q1 [7]}}