Differentiability Questions

Suppose the function $f(x)=x^n,n\ne 0$ is differentiable for all $x$. Then $n$ can be any element of the interval:

Consider the following statements:I. The derivative, where the function attains maxima or minima, is zero.II. If a function is differentiable at a point, then it must be continuous at that point.Which of the above statement(s) is/are correct?

The value of $c$ in Lagrange's theorem for the function $|x|$ in the interval $[-1,1]$ is: