Question

The function \( f(x) = (x(x - 2))^2 \) is increasing in the set

• A. \( (-\infty, 0) \cup (2, \infty) \)
• B. \( (-\infty, 1) \cup (2, \infty) \)
• C. \( (0, 1) \cup (2, \infty) \)
• D. \( (1, 2) \)

Hint:

To determine increasing or decreasing intervals, find the derivative and solve for where it is positive (increasing) or negative (decreasing).

Answer 1

The Correct Option is C

Step 1: Analyze the function.
We differentiate the function to find the intervals where the function is increasing. The derivative is positive in the intervals \( (0, 1) \) and \( (2, \infty) \).
Step 2: Conclusion.
Thus, the function is increasing in \( (0, 1) \cup (2, \infty) \). Final Answer: \[ \boxed{(0, 1) \cup (2, \infty)} \]