Q. 4
Find the intervals in which the function f given by f (x) = 2x2 – 3x is
(a) strictly increasing (b) strictly decreasing
Answer :
(a) It is given that function f(x) = 2x2 – 3x
⇒ f’(x) = 4x – 3
If f’(x) = 0, then we get,
So, the points 
divides the real line into two disjoint intervals, 
and 
So, in interval
, f’(x) = 4x -3 >0
Therefore, the given function (f) is strictly increasing in interval
.
(b) It is given that function f(x) = 2x2 – 3x
⇒ f’(x) = 4x – 3
If f’(x) = 0, then we get,
So, the points 
divides the real line into two disjoint intervals, 
and 
So, in interval 
f’(x) = 4x -3 < 0
Therefore, the given function (f) is strictly decreasing in interval
.
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