Mathematics 9709 · AS & A Level · Numerical solution of equations
Numerical solution of equations — practice question
A curve is defined by the parametric equations $x = t^2 + 3t + 1$, $y = t^4 + 1$. The point $P$ on the curve corresponds to parameter $p$. It is stated that the gradient of the curve at $P$ is $4$.
(a(i))[3]
Show that $p = \sqrt[3]{(2p + 3)}$ holds.
(a(ii))[2]
Check by calculation that $p$ is between $1.8$ and $2.0$.
(a(iii))[3]
Use an iterative formula derived from the equation in part (i) to determine $p$ correct to $2$ decimal places. Show the result of every iteration to $4$ decimal places.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Apply $\dfrac{dy}{dx}=\dfrac{y}{x}$, then set $\dfrac{dy}{dx}$ equal to $4$.” …