Let $$f : (-\infty, \infty) \to (-\infty, \infty)$$ be defined by $$f(x) = x^3 + 1$$. Statement 1: The function $$f$$ has a local extremum at $$x = 0$$. Statement 2: The function $$f$$ is continuous and differentiable on $$(-\infty, \infty)$$ and $$f'(0) = 0$$.

A

Statement 1 is true, Statement 2 is false.

B

Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation for Statement 1.

C

Statement 1 is true, Statement 2 is true, Statement 2 is not the correct explanation for Statement 1.

D

Statement 1 is false, Statement 2 is true.