Consider the polynomial function f(x)=x3−3x2+2.
Answer each of the following questions completely, showing all analytical work.
a. Calculate f′(x) and f′′(x).
b. Solve f′′(x)=0 to obtain all critical numbers associated with possible changes in concavity.
c. Determine the sign of f′′(x) on each interval determined in part (b), and classify the concavity of f on those intervals.
d. Verify each inflection point of f by confirming that the concavity changes. State the x–coordinate(s) and the corresponding point(s) (x,f(x)).