Answer is: option2

Solution:

We are given critical points of \( f(x) \):

• Relative minimum at \( (-4,2) \)
• Relative maximum at \( (-1,5) \)
• Relative minimum at \( (3,-3) \)
• No other critical points

The function has a relative minimum at \( (-4,2) \), meaning it decreases before \( x = -4 \) and increases after.

The function has a relative maximum at \( (-1,5) \), meaning it increases before \( x = -1 \) and decreases after.

The function has a relative minimum at \( (3,-3) \), meaning it decreases before \( x = 3 \) and increases after.

Given that \( f(-1) = 5 \) and it must cross the x-axis before reaching the next minimum, a zero exists in the interval \( (-1,3) \).

Since \( f(3) = -3 \) and it increases afterward, there must be a zero in the interval \( (3, \infty) \).

\( f(x) \) will have two zeroes between \( x = (-1,3) \) and \( (3, \infty) \).