For a function \( f(x) \), we know that \( f(15) = 74 \) and \( f'(15) = -3 \).

Estimate \( f(16) \), \( f(14) \), and \( f(18) \).

A) \( f(16) \approx 71 \), \( f(14) \approx 77 \), \( f(18) \approx 68 \)

B) \( f(16) \approx 71 \), \( f(14) \approx 77 \), \( f(18) \approx 80 \)

C) \( f(16) \approx 77 \), \( f(14) \approx 71 \), \( f(18) \approx 80 \)

D) \( f(16) \approx 77 \), \( f(14) \approx 71 \), \( f(18) \approx 68 \)

To estimate the values of f(16), f(14), and f(18), we can use the information provided about the function f(x) and its derivative. Since f'(15) = -3, it indicates that the function is decreasing at x = 15. Therefore, as we move away from x = 15, the function values are expected to decrease. Given that f(15) = 74, we can estimate f(16) and f(14) by subtracting 3 from f(15), resulting in f(16) ≈ 71 and f(14) ≈ 71.

To estimate f(18), we can consider the behavior of the function around x = 15. Since the function is decreasing and concave down at x = 15, moving further away from x = 15 will cause the function to decrease at a decreasing rate. Therefore, we can expect f(18) to be slightly higher than f(16). Considering this, we can estimate f(18) to be around 71 or slightly higher, leading to f(18) ≈ 80.

Hence, the correct option is c) f(16) ≈ 77, f(14) ≈ 71, f(18) ≈ 80.

Therefore, option c) is the correct choice as it aligns with the expected behavior of the function based on the given information about f(x) and f'(x) at x = 15.