Question

f(x)=x.e^-x is decreasing in
1) (-infinity, 1)
2) (1,infinty)
3) (-infinity, infinity)
4) (0,infinity)
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Answer 1

Step-by-step explanation:

3) (-infinity, infinity).........

Answer 2

f(x) = xe^-x

It is decreasing.

f'(x) < 0

(d/dx)(xe^-x) < 0

=> x (d/dx)(e^-x) + e^-x d/dx(x) < 0

=> -xe^-x + e^-x < 0

=> e^-x(1 - x) < 0

=> (1 - x) < 0

=> x > 1

∴ x ∈ (1,∞)

Option (2)