Continuity and Differentiation...

Hello,

I need help in figuring out the continuity of these weird looking function..

Please help!

Q1) Find the maximum and minimum value of the function:

f(x) = 4x^3 - x^2 - 4x + 2 on [ -1,1] and on [0,1]?

Q2) Let f: [0, infinity), -> R be defined by

f(x) = x sin (1/x) when x>0

and f(x) = 0 when x = 0.

Figure out if 'f' is continuous and differentiable at x = 0.

Q3) Define f: [-2,2] -> R by f(x) = |x^3 - 1|.

f: [-2,2] -> R by f(x) = |x^3| -1.

Determine the points where f is differentiable and find the derivative at those points?