Mathematics 9709 · AS & A Level · Numerical solution of equations
Numerical solution of equations — practice question
The diagram depicts a section of the curve $y = \frac{x^2}{1 + e^{3x}}$ together with its maximum point $M$. The $x$-coordinate of $M$ is written as $m$.
(i)[4]
Differentiate $\frac{dy}{dx}$ and hence show that $m$ satisfies the equation $x = \tfrac{2}{3}(1 + e^{-3x})$.
(ii)[2]
Demonstrate by calculation that $m$ lies between $0.7$ and $0.8$.
(iii)[3]
Apply the iterative formula based on the equation in part (i) to find $m$ correct to 3 decimal places. Give 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 method” …