Mathematics 9709 · AS & A Level · Numerical solution of equations
Numerical solution of equations — practice question
The graph of $y = x e^{2x} + 5 e^{-x}$ contains a minimum point $M$.
(a)[5]
Show that the $x$-coordinate of $M$ satisfies the equation $x = \tfrac{1}{3} \ln 5 - \tfrac{1}{3} \ln(1 + 2x)$.
(b)[3]
Use iteration process correctly on at least one occasion to find the $x$-coordinate of $M$ correct to 3 significant figures. Use an initial value of $0.35$ and give the result of each iteration to 5 significant figures.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Attempts to apply the product rule when differentiating $xe^{2x}$” …