| Exam Board | Edexcel |
|---|---|
| Module | F1 (Further Pure Mathematics 1) |
| Year | 2017 |
| Session | January |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Topic | Newton-Raphson method |
| Type | Newton-Raphson with verification |
| Difficulty | Standard +0.3 This is a straightforward Newton-Raphson application requiring differentiation of a multi-term function, one iteration of the formula, and verification by showing f(x) is sufficiently close to zero. While it involves fractional powers and requires careful arithmetic, it follows a standard algorithmic procedure with no conceptual challenges beyond routine A-level Further Maths content. |
| Spec | 1.07i Differentiate x^n: for rational n and sums1.09d Newton-Raphson method |
6.
$$f ( x ) = x ^ { 3 } - \frac { 1 } { 2 x } + x ^ { \frac { 3 } { 2 } } , \quad x > 0$$
The root $\alpha$ of the equation $\mathrm { f } ( x ) = 0$ lies in the interval [0.6, 0.7].
\begin{enumerate}[label=(\alph*)]
\item Taking 0.6 as a first approximation to $\alpha$, apply the Newton-Raphson process once to $\mathrm { f } ( x )$ to obtain a second approximation to $\alpha$. Give your answer to 3 decimal places.
\item Show that your answer to part (a) is correct to 3 decimal places.
\end{enumerate}
\hfill \mbox{\textit{Edexcel F1 2017 Q6 [7]}}