Let f(x) = -x^{3}\ln\!\left(x\right) . 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)

(b)

(c)

(d)

(e) the

** 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

You can earn partial credit on this problem.