Q. 1 S5.0( 1 Vote )
Find the intervals in which the following functions are increasing or decreasing.
f(x) = x4 – 4x
Answer :
Given:- Function f(x) = x4 – 4x
Theorem:- Let f be a differentiable real function defined on an open interval (a,b).
(i) If f’(x) > 0 for all 
, then f(x) is increasing on (a, b)
(ii) If f’(x) < 0 for all 
, then f(x) is decreasing on (a, b)
Algorithm:-
(i) Obtain the function and put it equal to f(x)
(ii) Find f’(x)
(iii) Put f’(x) > 0 and solve this inequation.
For the value of x obtained in (ii) f(x) is increasing and for remaining points in its domain it is decreasing.
Here we have,
f(x) = x4 – 4x
⇒ 
⇒ f’(x) = 4x3 – 4
For f(x) lets find critical point, we must have
⇒ f’(x) = 0
⇒ 4x3 – 4 = 0
⇒ 4(x3 – 1) = 0
⇒ x = 1
clearly, f’(x) > 0 if x > 1
and f’(x) < 0 if x < 1
Thus, f(x) increases on (1, ∞)
and f(x) is decreasing on interval x ∈ (–∞, 1)
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