<s>[INST] critical numbers of a complex function $ f(x) = 2 x - 5 x^{\frac{2}{5}} $ Critical numbers of $ f(x) = 2 x - 5 x^{2/5} $ are 1,$0$
How come $0$ is also a critical number?
I found the critical number 1 this way:
$f'(x) = 2 - 5 \ \frac {2}{5}  \ x^{-\frac{3}{5}}$ 
$ x^{\frac{3}{5}} = 1$
 [/INST] Critical values of a function occur where the derivative is zero or where the derivative is undefined.  
Since $f'(x)=2 - 2x^{\frac{-3}{5}} = 2 - \frac{2}{x^{\frac{3}{5}}} = 2 - \frac{2}{\sqrt[5]{x^3}}$
Hence, $f'(0)$ is undefined since we are dividing by zero.
Also, $f'(1) =0,$ therefore the critical values are 0 and 1.
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