Mathematics 9709 · AS & A Level · Numerical solution of equations
Numerical solution of equations — practice question
The diagram depicts the curve $y = (x - 4)e^{\frac{1}{2}x}$. At the point $P$, the curve’s gradient is $3$.
(a)[4]
Demonstrate that the $x$-coordinate of $P$ obeys the equation $x = 2 + 6e^{-\frac{1}{2}x}$.
(b)[2]
Check that the equation in part (a) has a root between $x = 3.1$ and $x = 3.3$.
(c)[3]
Use the iterative formula $x_{n+1} = 2 + 6e^{-\frac{1}{2}x_n}$ to find this root correct to $2$ decimal places. State each iteration to $4$ decimal places.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “At some point, give the correct derivative of $e^{x/2}$” …