Long Answer TypeFind 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.
Short Answer TypeLet 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
Here f(x) = x3 – 12x
∴ f ' (x) = 3x2 – 12 = 3 (x2 – 4) = 3 (x – 2) (x + 2)
For f (x) to be decreasing, f ' (x) < 0
∴ 3 (x – 2) (x + 2) < 0 or (x – 2) (x – 2) < 0
∴  – 2 < x < 2
f (x) is decreasing when – 2 < x < 2.
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
 is an increasing function of 
 in 
.
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