NDA 2026 · PYQ · Increasing and Decreasing Functions · easy
Let S and T be the sets where f(x) = x³/3 - 5x²/2 + 6x + 7 decreases and increases respectively. What is S equal to?
Answer
The correct answer is D: [2, 3]. f'(x) = (x-2)(x-3) ≤ 0 when 2 ≤ x ≤ 3. So f decreases on [2, 3], hence S = [2, 3].
- A.{x ≤ 2} ∪ {x ≥ 3}
- B.{x < 2} ∪ {x > 3}
- C.(2, 3)
- D.[2, 3]✓ Correct
f'(x) = (x-2)(x-3) ≤ 0 when 2 ≤ x ≤ 3. So f decreases on [2, 3], hence S = [2, 3].
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