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 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
Here f (x) = x2 - 4x + 6
∴ (x) = 2x – 4
f '(x) = 0 gives us 2x – 4 = 0 or x = 2
The point x = 2 divides the real line into two disjoint intervals (– ∞, 2). (2, ∞).
(a) In the interval (2, ∞), f ' (x) > 0
∴ f is strictly increasing in (2, ∞).
(b) In the interval (– ∞, 2), (x) < 0
∴ f is strictly decreasing in (– ∞, 2).
Note: Given function f is continuous at x = 2. which is the point joining the two intervals (– ∞, 2) and (2, ∞). Therefore f is decreasing in (– ∞, 2) and increasing in (2, ∞).
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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