Find the values of x for which y = [x(x – 2)]2 is an increasing function.
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