Question 153489
find the zeros of the function
<pre><font size = 4 color = "indigo"><b>
{{{f(x)=xe^(-x) -e^(-x)}}}

Set right side equal to zero:

{{{xe^(-x) -e^(-x)=0}}}

Factor out {{{e^(-x)}}}

{{{e^(-x)(x-1)=0}}}

Now we set each factor equal to zero.

Setting first factor = 0:

{{{e^(-x)=0}}}

That part has no solution since a positive
number raise to any power is always positive
and thus can never equal to 0.

Setting {{{x-1}}} = 0

{{{x-1=0}}}

{{{x=1}}}

So 1 is the only solution.

Edwin</pre>