Second Derivative Test Classification

00:00 4 marks

Consider the function \(f(x) = x^3 – 3x^2 + 2\). Find all the stationary points of \(f(x)\) and classify each as a local maximum or local minimum using the second derivative test.

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Hint

Differentiate \(f(x)\) to find \(f'(x)\), set \(f'(x)=0\) to locate stationary points, and then evaluate \(f”(x)\) at those points.

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Complete Answer

Stationary points: (0, 2) is a local maximum and (2, -2) is a local minimum.

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Answer Explanation Answer Explanation

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Common Errors Common Errors

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Second Derivative Test Classification

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Second Derivative Test Classification

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