Mathematics 9709 · AS & A Level · Numerical solution of equations
Numerical solution of equations — practice question
The graph given by $y = x\ln(4x + 1) - 3x$ has a single stationary point, $P$.
(a)[4]
Demonstrate that the $x$-coordinate of $P$ satisfies $x = \frac{2x + 0.75}{\ln(4x + 1)} - 0.25$.
(b)[2]
Use calculation to show that the $x$-coordinate of $P$ is between $1.8$ and $1.9$.
(c)[3]
Use an iterative formula based on the equation in part (a) to determine the $x$-coordinate of $P$ correct to 3 significant figures. Give each iteration result to 5 significant figures.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Try applying the product rule when differentiating $x\ln(4x+1)$” …