At which x does f(x) = x³ − 3x have a local minimum?
Answer and explanation
Correct answer: B. x = 1, where f′ = 0 and f″ > 0
- Step 1: f′(x) = 3x² − 3 = 0 gives x = ±1. Step 2. f″(x) = 6x: positive at x = 1 (minimum), negative at x = −1 (maximum). Answer: x = 1. Why not the others: x = −1 is the local maximum, and x = 0 is not a stationary point since f′(0) = −3.
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