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 2025 Mathematics question

Mathematics Application of Derivatives NDA 2025

Consider the following statements regarding the function : Statement-I : is decreasing on the intervals and . Statement-II : for all . Which one of the following is correct in respect of the above statements?

(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 correctCorrect
(D)Statement-I is not correct but Statement-II is correct

Answer: (C)

Solution

, which is negative for every . So is decreasing on each of the intervals and :

See the full step-by-step solution

Create a free account to read the complete working, and practise questions like this in a timed test.

Create a free account

Question ID VK-030230