As the title states I have to find the inflections and concavities of
$f(x) = (x-1)^{1/3} + (x+1)^{1/3}$
Since the second derivative
$f''(x) \ne 0 $ this should not have a inflection.
However upon looking at the formula I noticed that the inflection instead was identified using the original function $f(x)$
Where $x=0$ there apparently is a inflection. How did he figure out that from the first function, what's the relationship between the first function and it's second derivative? I would (evidently) stop after $f''(x) \ne 0 $ and conclude that there were no concavities. And all x-intersects are not necessarily inflection-points.
Many thanks whomever might help me!