I have to find the max. and min. values of the following function:

$\displaystyle y=3xe^{-x}+x$

When I take the first derivative, I get:

$\displaystyle y'=3e^{-x}-3xe^{-x}+1$

Though I'm not supposed to, I took a peak at the graph of the first derivative on my trusty graphing calculator and found that there are no critical values. So my question is, how do I show that there are no critical values using only calculation? (We are not allowed to use graphing calculators.)

(Sorry if I posted this in the wrong section. )