Mathematics 9709 · AS & A Level · Numerical solution of equations
Numerical solution of equations — practice question
The graph illustrates the curve $y = \frac{4 \ln x}{x^2 + 1}$ together with its stationary point $M$. Let the $x$-coordinate of $M$ be $m$.
(i)[5]
Find an expression for $\frac{dy}{dx}$ and hence demonstrate that $m = e^{0.5(1 + m^{-2})}$.
(ii)[3]
Use an iterative formula based on the equation in part (i) to find the value of $m$ correct to $4$ significant figures. Give the outcome of each iteration to $6$ significant figures.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Use quotient rule (or product rule) to find first derivative” …