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

Numerical solution of equations — practice question

(i)[3]

By sketching an appropriate pair of graphs, show that the equation $|3x| = 16 - x^4$ has two real roots.

(ii)[3]

Use the iterative formula $x_{n+1} = \sqrt[4]{(16 - 3x_n)}$ to determine one of the real roots correct to 3 decimal places. Show each iteration result to 5 decimal places.

(iii)[2]

Hence determine the coordinates of each intersection point of the graphs $y = |3x|$ and $y = 16 - x^4$, giving your answers correct to 3 decimal places.

Worked solution & mark scheme

This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: Draw a recognisable sketch of $y=16-x^4$

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