191.

Find intervals in which the function given by 

is (a) strictly increasing (b) strictly decreasing.

Find the intervals in which the function  is increasing or decreasing.

Separate  into sub-intervals in which the function f (x) = sin 3x is increasing or decreasing.

Find the intervals in which the following function is increasing or decreasing:
f (x) = sinx – cosx, 0 < x < 2. 

Find the intervals in which the following function is increasing or decreasing
f (x) = (x + 2) e^–x 

Find the intervals in which the function (x + 1)³ (x – 1)³ is strictly increasing or decreasing.

Let f be a function defined on [a, b] such that f ' (x) > 0, for all x ∊ (a, b). Then prove that f is strictly increasing function of (a, b).

On which of the following intervals is the function f given by f (x) = x¹⁰⁰ + sin x – 1 strictly decreasing?
(A)   (0, 1)     (B)       (C)      (D) None of these