Mathematics : Application of Derivatives

Prove that  is an increasing function of  in .

Find the intervals in which the function f is given by
                         
is (i) increasing    (ii)  decreasing

Determine the values of x for which the function  is increasing and for which it is decreasing.

Let I be any interval disjoint from (– 1, 1). Prove that the function f given by  is strictly increasing on I.

Find the intervals in which the following function is decreasing:
f (x) = x³ – 12x

Find the intervals in which the function f given by f(x) = 2x² – 3x is
(a) strictly increasing    (b) strictly decreasing

Find the intervals in which the function f given by f(x) = x² – 4x+6  is
(a) strictly increasing    (b) strictly decreasing

Find the intervals in which the following functions are strictly increasing or decreasing:
x²+ 2x – 5

Find the intervals in which the following functions are strictly increasing or decreasing:
10 – 6x – 2x²