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Question

Find the intervals of monotonicity for the following function.
f(x)=x2ex

A
I in (0,2) & D in (,0)(2,)
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B
I in (0,3) & D in (,0)(3,)
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C
I in (0,4) & D in (,0)(4,)
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D
I in (0,1) & D in (,0)(1,)
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Solution

The correct option is B I in (0,2) & D in (,0)(2,)
Given, f(x)=x2ex

f(x)>0 implies
x2.ex+2x.ex>0
ex(2xx2)>0
Hence, x(2x)>0
x>0 and x<2.
Hence, the function is increasing for (0,2) and decreasing for the xR(0,2).

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