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Which of the following situations is impossible for a function $f$?
$f''(c)=0$ but $c$ is not an inflection point
Every point in $f$'s domain is a critical point
$c$ is a local maximum but $f'(c)\not=0$
$c$ is an inflection point but $f''(c)\not=0$
$f(c)$ undefined but $c$ is a local extremum