Question

Find all intervals of increasing, decreasing concavity
f(x)=x^3-6x^2+12x

Answer 1

Better perhaps to write your question as follows:

"Find all intervals on which the following function is (1) increasing and (2) decreasing. Determine the inflection points, if any, as well as the direction of concavity of the graph on all intervals determined by these inflection points.

1. Intervals on which the function is increasing or decreasing:
a) find the first derivative, f '(x)
b) set this derivative = to 0; solve for the "critical values."
c) graph these c. v. on a number line.
d) identify all of the intervals on this number line determined by the c. v.

Answer 2

(To be continued)