Answer is: option3
\( f'(2) < f(2) < f''(2) \)Solution:
- The function is decreasing at \( x = 2 \Rightarrow \) so the slope \( f'(2) < 0 \)
- The curve is concave up at \( x = 2 \Rightarrow \) meaning the graph is curving upward, so: \( f''(2) > 0 \)
Given \( f(2) = 0 \), we now have:
- \( f'(2) < 0 \)
- \( f(2) = 0 \)
- \( f''(2) > 0 \)
From least to greatest:
\( f'(2) < f(2) < f''(2) \)
Correct Answer: \( f'(2) < f(2) < f''(2) \)