For the function f(x)=∣x3−3x∣, answer the following.
a. (a) Express f as an explicit piecewise function by considering the sign of x3−3x.
b. (b) Find all values of x where either f′(x)=0 or f is not differentiable.
c. (c) Classify each point obtained in part (b) as a point of local maximum, local minimum or neither, giving reasons in each case.