Mathematics 9709 · AS & A Level · Numerical solution of equations
Numerical solution of equations — practice question
The curve is defined by $y = \frac{3x^2}{x^2 + 4}$. At the point on the curve where the $x$-coordinate is positive and equal to $p$, the gradient is $\tfrac{1}{2}$.
(i)[5]
Show that this gives $p = \sqrt{\frac{48p - 16}{p^2 + 8}}$.
(ii)[2]
Show, by calculation, that $2 \le p \le 3$.
(iii)[3]
Use an iterative formula based on the equation in part (i) to find $p$ correct to $4$ significant figures. Give each iterative value to $6$ significant figures.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Apply the quotient rule, or an equivalent method” …