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?

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