Mathematics 9709 · AS & A Level · Numerical solution of equations
Numerical solution of equations — practice question
The curve is defined by $y = 6xe^{\frac{1}{3}x}$. At the point on it where the $x$-coordinate is $p$, the gradient is $40$.
(i)[4]
Demonstrate that $p = 3\ln\left(\frac{20}{p + 3}\right)$.
(ii)[2]
Use calculation to show that $3.3 \le p \le 3.5$.
(iii)[3]
Use an iterative formula based on the equation in part (i) to determine $p$ correct to $3$ decimal places. Record the outcome of each iteration to $5$ decimal places.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Apply the product rule to get the form $k_1 e^{\frac13x}+k_2 x e^{\frac13x}$” …