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# Find the intervals in which f (x) =|x-2|x2is strictly increasing and strictly decreasing.

bharat bajaj IIT Delhi
7 years ago
Case 1 : Say x>2,
f(x) = (x-2) x^2
df/dx = 3x^2 - 4x > 0 for strictly increasing
so x belongs to : x>4/3 or x<0 for strictly increasing. Hence x>2 for strictly increasing.
Case 2 : x<2
f(x) = (2-x)x^2
df/dx = 4x - 3x^2
For strictly increasing, df/dx >0
4x-3x^2 >0 or
3x^2 - 4x < 0
Hence, x belongs to (0,4/3)
Hence Strictly increasing : x in range (0,4/3) union (2,inf)
Strictly decreasing : (-inf,0) union (4/3,2)
Thanks & Regards
Bharat Bajaj
`F(x) = (x-2)x2 ; x>=2; Strictly increasing(2-x)x2 ; x<2; Strictly increasingThank YouRuchiIIT DelhiAskiitians Faculty`