What to do if the critical point is not a real number? I have a function and I already differentiate it, but when I put it equals to zero I don't get a real number. What am I doing wrong?
$f(x) = x\sqrt{x^2+1}$
$f'(x) = \sqrt{x^2+1}+\frac{x^2}{\sqrt{x^2+1})}$
$f'(x) = \frac{2x^2+1}{\sqrt{x^2+1}}$
Then I equalizes it to 0
$\frac{2x^2+1}{\sqrt{x^2+1}}=0$
$2x^2+1=0$
$2x^2=-1$
$x^2=-1/2$
So I don't know what to do next. 
When reach the second derivative I get the same problem. What it means?

The test for stationary points is like this:  

If $f$ has a stationary point at $x$, then  $f'(x)=0$. 

So if $f'(x)$ isn't zero for any $x$, what would that mean?
