Is the local max and local min of f(x)=y=(x^3) + 1 same as the inflection point

They all worked out to be (0,1). I need clarification.

No, it has no extrema.

Edit: look:
y' = 3x^2
x = 0
y" = 6x
y"(0) = 0
so there is no turning point or critical point

Any f(x) has a maximum, a minimum, or an inflexion, where df(x)/dx = 0.
It's a maximum if d^2f(x)/dx^2 < 0,
a minimum if d^2f(x)/dx^2 > 0
and an inflection if d^2f(x)/dx^2 = 0

f(x) = x^3 + 1 satisfies d^2f(x)/dx^2 = 0 at (0, 1) so this is an inflection, NOT a max or min