Mathematics · JEE | APPLICATION OF DERIVATIVES

In the graph representing local extrema and points of non-differentiability, let \( c_2 \) be a point of local minima and \( c_3 \) be a point of non-differentiability. Which of the following correctly describes the behavior of \( f'(x) \) around \( c_2 \)?

1. A
   \( f'(x) \) changes from positive to negative at \( c_2 \)
2. B
   \( f'(x) \) remains negative throughout the neighborhood of \( c_2 \)
3. C
   \( f'(x) \) remains positive throughout the neighborhood of \( c_2 \)
4. D
   \( f'(x) \) changes from negative to positive at \( c_2 \)