Consider the polynomial function f(x) = x^4 3x^3 + 3x^2 whose domain is (, )

(a)Find the intervals on whichfis increasing. (Enter you answer as a comma-separated list of intervals.)

Find the intervals on whichfis decreasing. (Enter you answer as a comma-separated list of intervals.)

(b)Find the open intervals on whichfis concave up. (Enter you answer as a comma-separated list of intervals.)

Find the open intervals on whichfis concave down. (Enter you answer as a comma-separated list of intervals.)

(c)Find the local extreme values off. (If an answer does not exist, enter DNE.)local minimum value

local maximum value

(d)Find the global extreme values offon the closed, bounded interval

[1, 2].

global minimum value

global maximum value

(e)Find the points of inflection off.smallerx-value

(x,f(x))

=

largerx-value

(x,f(x))

=

(f)Sketch the graph offon

[1, 2]

using this information