The interval in which y = x 2 e –x is increasing is

Question

Philoid · Accepted 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).