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

Numerical solution of equations — practice question

(i)[3]

Use sketches of two suitable graphs to 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. Present the outcome of each iteration to $5$ decimal places.

(iii)[2]

Hence find the coordinates of each point where the graphs $y = |3x|$ and $y = 16 - x^4$ intersect, with 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 sketch that is recognisably $y = 16 - x^4$

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