Question

When does f'(x)=0 and when does f'(x)= Doesn't exist/ Undefined? f'(x) = ((2-x^2)/(x^4))

Answer 1

x = +/- 2 then f' = 0
x = 0 then f' DNE

Answer 2

That's what I got originally but I'm wondering if maybe it's \[x= +/- \sqrt{2}\]

Answer 3

Ah, sorry. I made it a mistake
\[f \prime = \frac{2 - x^2} {x^4}\]

f' = 0 --> x^2 = 2 --> \[x = \pm \sqrt{2}\]

Answer 4

it is undefined when x = 0 (you can't divide by 0 ) 0^4 = 0...
and linh is correct for when f'(x) = 0 , good work