Q. 193.9( 27 Votes )

The interval in w A. (– ∞, ∞)

B. (– 2, 0)

C. (2, ∞)

D. (0, 2)

Answer :

it is given that y = x2 e–x


then


Now if


x = 0 and x =2


The points x = 0 and x= 2 divide the real line into three disjoint intervals ie, (-∞,0), (0,2) and (2,∞).


In interval (-∞,0) and (2,∞),


f’(x) < 0 as e-x is always positive.


Therefore, f is decreasing on (-∞,0) and (2,∞).


In interval (0,2), f’(x)>0


Therefore, f is strictly increasing in interval (0.2).

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