Answer :

It is given that y = [x(x – 2)]2, then,


= 4x(x - 2)(x - 1)


Now if


x = 0, 1,2


So, the points x = 0, x =1 and x = 2 divides the real line into four disjoint intervals,


(-∞,0), (0,1), (1, 2) and (2,∞).


So, in interval(-∞,0),(1,2)


< 0


Therefore, the given function (f) is strictly decreasing in intervals .


So, in interval (0,1) and (2,∞)



Therefore, the given function (f) is strictly increasing for 0 < x < 1 and x>2


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