Answer is: option3
(C)Solution:
1. Understand the shape of \( f(x) \)
- \( f(x) \) increases, reaches a local maximum, then decreases, reaches a local minimum, then increases again.
- Therefore, \( f'(x) = 0 \) at the local maximum and local minimum (i.e., where the slope is zero).
So, we’re looking for a graph of \( f'(x) \) that:
- Is zero at two points (corresponding to the maximum and minimum of \( f(x) \)),
- Is positive where \( f(x) \) is increasing,
- Is negative where \( f(x) \) is decreasing.
This matches option C