Cоnsider the functiоn $$style{fоnt-size:18pt}{f(x) = x^3-4x^2+4x+1.}$$ (а) Find the criticаl points of $$style{font-size:18pt}{f.}$$ (b) Stаte the intervals of increase and decrease of $$style{font-size:18pt}{f.}$$ (c) Find the local maximum and minimum values of $$style{font-size:18pt}{f.}$$ (d) Find the intervals of concavity of $$style{font-size:18pt}{f.}$$ (e) Find all inflection points of $$style{font-size:18pt}{f.}$$ In each case give enough detail to fully justify your answer, including phase lines where appropriate.