Mathematics 9709 · AS & A Level · Numerical solution of equations
Numerical solution of equations — practice question
The diagram displays a segment of the curve $y = \frac{x^{2}}{1 + e^{3x}}$ together with its maximum point $M$. Let the $x$-coordinate of $M$ be $m$.
(i)[4]
Find $\frac{dy}{dx}$ and hence prove that $m$ satisfies the equation $x = \tfrac{2}{3}(1 + e^{-3x})$.
(ii)[2]
Show by calculation that $m$ is between $0.7$ and $0.8$.
(iii)[3]
Use an iterative formula based on the equation in part (i) to determine $m$ correct to $3$ decimal places. Give the outcome of each iteration to $5$ decimal places.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Apply the quotient rule or an equivalent valid approach” …