Question

Let \( \phi(x) = f(x) + f(2a - x) \), \( x \in [0, 2a] \) and \( f'(x)>0 \) for all \( x \in [0, a] \). Then \( \phi(x) \) is:

• A. increasing on \( [0, a] \)
• B. decreasing on \( [0, a] \)
• C. increasing on \( [0, 2a] \)
• D. decreasing on \( [0, 2a] \)

Hint:

To determine if a function is increasing or decreasing, compute its derivative and analyze its sign over the interval. Use symmetry and test with simple functions like quadratics to understand behavior.