Mathematics 9709 · AS & A Level · Numerical solution of equations
Numerical solution of equations — practice question
For the curve with equation $e^{2x} - 18x + y^3 + y = 11$, the stationary point is $(p, q)$.
(a)[4]
Determine the exact value of $p$.
(b)[2]
Show that $q = \sqrt[3]{2 + 18 \ln 3 - q}$.
(c)[2]
Show by calculation that $q$ lies between $2.5$ and $3.0$.
(d)[3]
Use an iterative method, based on the equation in part (b), to find $q$ correct to $4$ significant figures. Give each iteration result to $6$ significant figures.
Worked solution & mark scheme
This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Differentiate $y^3$ so that it becomes $3y^2\frac{dy}{dx}$” …