Consider the function

f(x) =x^1/3(x+ 2)^2/3

whose domain is

(,).

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

(,2],[23,)

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

[2,23]

(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.)

(0,)

(c)Find the local extreme values off. (Round your answers to three decimal places.)local minimum value

1.058

local maximum value

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

[3, 2].

(Round your answers to three decimal places.)global minimum value

global maximum value

(e)Find the points of inflection off. (If an answer does not exist, enter DNE.)