Let S and T be the sets where f(x) = x³/3 - 5x²/2 + 6x + 7 decreases and increases respectively. What is T equal to?
A.{x ≤ 2} ∪ {x ≥ 3}✓ Correct
B.{x < 2} ∪ {x > 3}
C.(2, 3)
D.[2, 3]
Explanation
f'(x) = x² - 5x + 6 = (x-2)(x-3). f'(x) ≥ 0 when x ≤ 2 or x ≥ 3 (increasing on closed intervals where derivative is non-negative). So T = {x ≤ 2} ∪ {x ≥ 3}.
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