Mathematics 9709 · AS & A Level · Numerical solution of equations

Numerical solution of equations — practice question

The curve whose equation is $y = x e^{2x} + 5e^{-x}$ has a minimum point $M$.
(a)[5]

Show that the $x$-coordinate of $M$ is given by the equation $x = \frac{1}{3}\ln 5 - \frac{1}{3}\ln(1 + 2x)$.

(b)[3]

Use iteration, based on the equation in part (a), to determine the $x$-coordinate of $M$ correct to 3 significant figures. Begin with an initial value of $0.35$ and state 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: An attempt is made to use the product rule when differentiating $xe^{2x}$

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