Critical numbers of this derivative

[opticaltempest]

I have the function \[y = \sqrt x - 4\ln (x)\]

I find the derivative to be \[y' = \frac{{\sqrt x - 8}}{{2x}}\]

When finding the critical numbers of y' I look for where the derivative
is equal to zero or where the derivative is undefined. So where y' is
equal to zero is when x=64. y' is undefined when x=0, but when x=0
the original function is also undefined. Since x=0 makes the original
function undefined can I exclude it from my critical points? I am thinking
I am able to since x=0 isn't even in the domain of y.

Thanks

 

[HallsofIvy]

Yes, that is correct. By the way, the phrase "critical numbers of y' " is not correct. What you have found are the critical numbers of y itself, not its derivative.

 

[opticaltempest]

Thanks HallsofIvy