Derivatives Questions

If the function f(x) = x² − kx is monotonically increasing in the interval (1, ∞), then which one of the following is correct?

Consider the following 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?

For the following two (02) items:

Let the function f(x) = |x - 3|+|x - 4|be defined on the interval [0, 5]. Consider the following statements:

I. The function is differentiable at x = 3.

II. The function is differentiable at x = 4.

 Which of the statements given above is/are correct?

For the following two (02) items: Let the function f(x) = |x - 3|+|x - 4|be defined on the interval [0, 5].

What is dy/dx at x = 3.5 equal to?

For the following two (02) items:

What is f ’(-1) equal to?

For the following three (03) items:

 If x = sinθ, then what is dy/dx equal to?

For the following three (03) items:

What is d²y/dx² at x = 0 equal to?

For the following three (03) items:

For the following three (03) items: Consider the function f(x) = x|x|. Consider the following statements:

I. The function is increasing in the interval (-∞, ∞).

 II. The function is differentiable at x = 0. Which of the statements given above is/are correct?

Direction for Questions (119-120): Consider the following for the two (02) items that follow:What is equal to?