Mathematics 9709 · AS & A Level · Numerical solution of equations
Numerical solution of equations — practice question
The diagram depicts a section of the curve with equation $y = \dfrac{x^3}{x + 2}$. At the point $P$, the gradient of the curve equals $6$.
(a)[4]
Show that the $x$-coordinate of $P$ obeys the equation $x = \sqrt[3]{12x + 12}$.
(b)[2]
Use calculation to show that the $x$-coordinate of $P$ lies between $3.8$ and $4.0$.
(c)[3]
Apply an iterative formula, derived from the equation in part (a), to determine the $x$-coordinate of $P$ correct to $3$ significant figures. Show each iteration to $5$ significant figures.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Use the quotient rule to differentiate” …