Standard +0.3 This is a straightforward application of the Newton-Raphson formula requiring differentiation of a function with fractional and negative powers, then one iteration of the process. While the derivative involves multiple terms (x^{1/2} and x^{-2}), this is standard FP1 fare with no conceptual challenges—just careful algebraic manipulation and calculator work.
4.
$$f ( x ) = 2 x ^ { \frac { 1 } { 2 } } - \frac { 6 } { x ^ { 2 } } - 3 , \quad x > 0$$
A root \(\beta\) of the equation \(\mathrm { f } ( x ) = 0\) lies in the interval \([ 3,4 ]\).
Taking 3.5 as a first approximation to \(\beta\), apply the Newton-Raphson process once to \(\mathrm { f } ( x )\) to obtain a second approximation to \(\beta\). Give your answer to 3 decimal places.
4.
$$f ( x ) = 2 x ^ { \frac { 1 } { 2 } } - \frac { 6 } { x ^ { 2 } } - 3 , \quad x > 0$$
A root $\beta$ of the equation $\mathrm { f } ( x ) = 0$ lies in the interval $[ 3,4 ]$.\\
Taking 3.5 as a first approximation to $\beta$, apply the Newton-Raphson process once to $\mathrm { f } ( x )$ to obtain a second approximation to $\beta$. Give your answer to 3 decimal places.\\
\hfill \mbox{\textit{Edexcel FP1 2014 Q4 [5]}}