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Show that f(x)=(x-1)e^x+1 is an increasi...

Show that `f(x)=(x-1)e^x+1` is an increasing function for all `x >0` .

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Verified by Experts

We have given
`f(x)=(x-1)e^x+1`
`impliesf'(x)=xe^x`
As given `x` > `0`
`implies e^x` > `0`
`implies xe^x` >` 0`
`implies f’(x)` > `0`
So, `f(x)` is increasing for all `x>0`
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