Let f(x)=x3−3x2+2 for all real x.
a. Calculate f′(x).
b. Determine every critical point of f on (−∞,∞).
c. For each critical point, classify it as a relative minimum or relative maximum. Provide clear reasoning based on the change in sign of f′(x).
d. Arrange the relative extrema from lowest to highest f-value.