1. Suppose we have f(x)=3x^4 -16 x^3 + 24 x^2.
(a) (8 pts) Find all critical points of f(x)
b) (8 pts) Make a table showing the intervals on which the graph of f(x) is increasing or decreasing. For this, use the template below, completing each item for each of your intervals. Interval Test value of f0 (x) Sign of f0 (x) Increase/decrease behavior of f(x)
(c) (8 pts) Use the first derivative test to identify each of the critical points of f(x) that you found in part (a) as a local maximum, a local minimum, or neither. Justify your conclusions by referring to your table in (b).