Question

Find the maximum value of the function f(x)=xe^-x.

Answer 1

to find an extremum you differentiate function
\[\frac{ d }{ dx }xe ^{-x}=e ^{-x}+x \times(-e^{-x})=e^{-x}-xe^{-x}\]

Answer 2

\[\frac{ df }{ dx }=0\] \[e^{-x}-xe^{-x}=0\] \[e^{-x}(1-x)=0\] \[x=1\]

Answer 3

But the answer should be 1/e.

Answer 4

put x=1 in f(x)

Answer 5

1*e^(-1)=1/e