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” …