critical values are where a derivative is equal to 0 or is undefined.

any derivative can have critical values ... it just depends on what you want to accomplish.

for the 1st derivative ...

if a function f(x) has extrema, then they are located at critical values of f'(x)

for the second derivative ...

if a function f(x) has inflection points, then they are located at critical values of f''(x)

note that the converse to both of the above statements is not necessarily true.

for your function ...

is equal to 0 at x = 0 (just set the numerator equal to 0)

y' is defined for all x.

so, there is only one critical value for y' ... x = 0 , and using the 1st derivative test for extrema, the original function has a minimum at x = 0.

y'' = 0 at

y'' is defined for all x.

y'' has critical values at

the original function has inflection points at both critical values since y'' changes sign at each value.