Mathematics 9709 · AS & A Level · Numerical solution of equations

Numerical solution of equations — practice question

The curve is given by $y = x^3 e^{0.2x}$ for $x \ge 0$. At the point $P$ on this curve, the gradient is $15$.
(a)[4]

Show that the $x$-coordinate of $P$ satisfies the equation $x = \sqrt{\frac{75e^{-0.2x}}{15 + x}}$.

(b)[2]

Use the equation from part (a) to demonstrate by calculation that the $x$-coordinate of $P$ lies between $1.7$ and $1.8$.

(c)[3]

Apply an iterative formula based on the equation in part (a) to determine the $x$-coordinate of $P$ correct to $4$ significant figures. State the result of each iteration to $6$ significant figures.

Worked solution & mark scheme

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