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The function f(x) = x³ − 27x + 4, 1 ≤ x ≤ 6 has

1. Maxima point
2. Minima point
3. Saddle point
4. Inflection point

Correct answer: Minima point

Solution

f'(x) = 3x^2 - 27 = 0 gives x = 3 (within 1<=x<=6), and f''(x) = 6x = 18 > 0, so x = 3 is a local minimum. The function therefore has a minima point, option index 1, not an inflection point.

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