Which one of the following is correct ? The function
`f(x) =(x-1)e^(x)+1` is

Options

A. negative for all `x gt 0`
B. positive for all `x gt 0`
C. increasing for all `x gt 0`
D. decreasing for all x

Answer

C

Explanation

The given function is
`f(x) =(x-1)e^(x)+1`
`rarr f(x) =(x-1)e^(x)+e^(x` ltrbgt `=(x-1+1)e^(x)=xe^(x)`
Thus it is clear that f(x) is increasing for all x