What is T equal to ?
For the next two (02) items that follow : Let S and T be the sets where \( f(x) = \frac{x^3}{3} - \frac{5x^2}{2} + 6x + 7 \) decreases and increases respectively.
- A. \{x \le 2\} \cup \{x \ge 3\} ✓
- B. \{x < 2\} \cup \{x > 3\}
- C. (2, 3)
- D. [2,3]
Correct Answer: A. \{x \le 2\} \cup \{x \ge 3\}
Explanation
Find the derivative: \( f'(x) = x^2 - 5x + 6 = (x-2)(x-3) \). The function is increasing when \( f'(x) \ge 0 \), which corresponds to \( x \le 2 \) or \( x \ge 3 \).
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