# Calculus problem

Let f(x)=x^(4)â?'6x^(3)+12x^(2). Find (a) the intervals on which f is increasing, (b) the intervals on which f is decreasing, (c) the open intervals on which f is concave up, (d) the open intervals on which f is concave down, and (e) the x-coordinates of all inflection points.

(a) f is increasing on the interval(s) =

(b) f is decreasing on the interval(s) =

c) f is concave up on the open interval(s) =

(d) f is concave down on the open interval(s) =

(e) the x coordinate(s) of the points of inflection are =

Notes: In the first four boxes, your answer should either be a single interval, such as [0,1), a comma separated list of intervals, such as (-inf, 2), (3,4], or the word "none".

In the last box, your answer should be a comma separated list of x values or the word "none".

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#### Solution Summary

The expert examines a calculus problem for intervals.