f(x)=x

3

lnx,x>0.

f(x)=x3lnx,x>0.

a) Determine the intervals on whichf

fis concave up and concave down.

f

fis concave up on:

f

fis concave down on:

b) Based on your answer to part (a), determine the inflection points off

f. Each point should be entered as anordered pair(that is, in the form(x,y)

(x,y)).

(Separate multiple answers by commas.)

c) Find the critical numbers off

fand use the Second Derivative Test, when possible, to determine the relative extrema. List only thex

x-coordinates.

Relative maxima at:(Separate multiple answers by commas.)

Relative minima at:(Separate multiple answers by commas.)