Mathematics 9709 · AS & A Level · Numerical solution of equations
Numerical solution of equations — practice question
The curve is given by $y = 6x e^{\frac{1}{3}x}$. At the point on the curve where the $x$-coordinate is $p$, the gradient of the curve equals $40$.
(i)[4]
Show that $p = 3 \ln\left(\frac{20}{p + 3}\right)$.
(ii)[2]
Show by calculation that $3.3 \le p \le 3.5$.
(iii)[3]
Use an iterative formula based on the equation in part (i) to determine the value of $p$ correct to 3 decimal places. State the result 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 an expression of the form $k_1e^{\frac{1}{3}x}+k_2xe^{\frac{1}{3}x}$” …