Question
Consider the following statements regarding the function f(x) = 1 x - 5 : Statement-I: f(x) is decreasing on the intervals x 5. Statement-II: f'(x) > 0 for all x 5. Which one of the following is correct in respect of the above statements?
NDA
Mathematics
Application of Derivatives
2025
NDA 2025 (Phase 2)
NDA Mathematics Question (2025) — Solution
Options
- A. Both Statement-I and Statement-II are correct and Statement-II explains Statement-I
- B. Both Statement-I and Statement-II are correct but Statement-II does not explain Statement-I
- C. Statement-I is correct but Statement-II is not correct
- D. Statement-I is not correct but Statement-II is correct
Answer
C. Statement-I is correct but Statement-II is not correct
Step-by-step solution
Given the function f(x) = 1 x - 5 . Differentiating with respect to x, we get: f'(x) = d dx (x - 5)^ -1 = -1(x - 5)^ -2 = - 1 (x - 5)^2 For all x 5, (x - 5)^2 > 0, which implies f'(x) Since f'(x) Therefore, Statement-I is correct. Statement-II claims that f'(x) > 0 for all x 5, which contradicts our finding that f'(x) Hence, Statement-I is correct but Statement-II is not correct. Answer: Statement-I is correct but Statement-II is not correct
Related: Mathematics — Application of Derivatives · All PYQ Banks