Consider the following statements regarding the function f(x) = 1/(x - 5)

Statement-I: f(x) is decreasing on the intervals x < 5 and x > 5

Statement-II: f''(x) > 0 for all x ≠ 5.

Which one of the following is correct in respect of the above statements?

Consider the following statements:

Statement-I: The function  $f(x)=\frac{x^{3}+128}{x}$ has a minimum value 48 at x = 4

Statement-II: As x increases through 4, f'(x) changes sign from positive to negative.

Which one of the following is correct in respect of the above statements?

Consider the following for the two (02) items that follow: Let ABC be a triangle right-angled at B and AB+AC = 3 units.

What is ∠A equal to if the area of the triangle is maximum?

Consider the following for the two (02) items that follow: Let ABC be a triangle right-angled at B and AB+AC = 3 units.

What is the maximum area of the triangle?