Consider the polynomial function defined by .

MATHEMATICS · Multi-part · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

Consider the polynomial function

g

defined by

g(x) = x^4 - 4x^3 + 6x^2 + 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.