Mathematics 9709 · AS & A Level · Numerical solution of equations
Numerical solution of equations — practice question
The diagram displays the curve $y = xe^{2x} - 5x$ together with its minimum point $M$, for which $x = \alpha$.
(a)[3]
Show that $\alpha$ satisfies the equation $\alpha = \frac{1}{2} \ln \left( \frac{5}{1 + 2\alpha} \right)$.
(b)[2]
Confirm by calculation that $\alpha$ lies between $0.4$ and $0.5$.
(c)[3]
Use an iterative formula based on the equation in part (a) to find $\alpha$ correct to $2$ decimal places. Show the value obtained at each iteration to $4$ decimal places.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Apply the correct product rule” …