What is S 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: D. [2,3]
Explanation
The function decreases when \( f'(x) \le 0 \). From \( f'(x) = (x-2)(x-3) \), this occurs in the closed interval.
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