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

Numerical solution of equations — practice question

For the curve given by $y = \frac{x^3}{e^x - 1}$, there is a stationary point when $x = p$, where $p > 0$.
(a)[3]

Show that this gives $p = 3(1 - e^{-p})$.

(b)[2]

Confirm by calculation that $p$ lies between $2.5$ and $3$.

(c)[3]

Use an iterative formula derived from the equation in part (a) to find $p$ correct to $2$ decimal places. Give the outcome of 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 quotient rule or product rule

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