Calculus

To solve the problem, we need to find the interval where the function is increasing.

1. Take the First Derivative:
To determine where a function is increasing, we compute its first derivative:

2. Set Derivative Equal to Zero to Find Critical Point:
Set :

This divides the real number line into two intervals: and

3. Test the Sign of the Derivative:
- For : Choose , then → Negative → Function is decreasing.
- For : Choose , then → Positive → Function is increasing.

4. Conclusion:
The function is increasing in the interval . Since option (D) is , and derivative at is 0, which is a stationary point, the function is not increasing at exactly . So the strictly increasing interval is , but the closest matching answer is:
(D) [2, ∞)

Final Answer:
The function is increasing in the interval [2, ∞).