Approximating Stationary Points Numerically

00:00 4 marks

Consider the function \(f(x) = x^3 – 6x^2 + 9x + 15\). Using the Newton-Raphson method, approximate the values of \(x\) where the derivative \(f'(x)\) equals zero. Perform at least three iterations for each stationary point and provide your answers to 3 significant figures.

Hint Hint

Hint

Recall the Newton-Raphson iteration formula: \(x_{n+1} = x_n – \frac{f'(x_n)}{f”(x_n)}\). Apply this to \(f'(x)\) to find where \(f'(x) = 0\).

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Complete Answer

The stationary points are approximately at \(x \approx 1.00\) and \(x \approx 3.00\).

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