Consider the polynomial function g defined by
g(x)=x4−4x3+6x2+1.
(a) Determine g′′(x).
(b) Solve g′′(x)=0 and use the result to locate all possible inflection points.
(c) State the intervals on which the graph of g is concave up and those on which it is concave down. Then give the exact coordinates of every inflection point.