35. The graph of \( f \) is shown in the figure above. Which of the following could be the graph of \( f' \)?






Answer is: option3

(C)

Solution:

1. Understand the shape of \( f(x) \)

  1. \( f(x) \) increases, reaches a local maximum, then decreases, reaches a local minimum, then increases again.
  2. 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:

  1. Is zero at two points (corresponding to the maximum and minimum of \( f(x) \)),
  2. Is positive where \( f(x) \) is increasing,
  3. Is negative where \( f(x) \) is decreasing.

This matches option C

Previous Next