question_answer 1)

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

Answer:

Let y = f(x) = [x (x ? 2)]2 = (x2 ? 2x)2        = 2 (x2 ?2x) (2x ? 2)       = 4x (x ?2) (x? 1)       f?(x) = 0       Intervals are :       When       f?(x) = 0       Intervals are :       When       f?(x) = 4(?)(?)(?) < 0       When       f?(x) = 4(+) (?)(?) > 0       When       f?(x) = 4(+)(?) (+) < 0       When       f?(x) = 4(+) (+)(+) > 0        is an increasing function.