Concave down on #(-oo,-5)# and on #(0,5)#
Concave up on #(-5,0)# and on #(5,oo)#
Inflection point #(0,0)#
#f'(x) = (x^2(x^2-75))/(x^2-25)^2#
#f'(x)# DNE at #x=+-5# but those are not in the domain, so they are not critical.
#f'(x) = 0# at #x=0# and at #x + +-sqrt75# which are in the domain, so they are all critical numbers.
#f''(x) = (50x(x^2+75))/(x^2-25)^3# could change sign at #0# and at #+-5#
On #(-oo,-5)#, #f''(x) < 0#, so #f# is concave down.
On #(-5,0)#, #f''(x) > 0#, so #f# is concave up.
On #(0,5)#, #f''(x) < 0#, so #f# is concave down.
On #(5,oo)#, #f''(x) < 0#, so #f# is concave up.
The concavity changes at #x=-5#, #0# and #5#. An inflection point is a point of the graph where concavity changes. Since #-5# and #5# are not in the domain of #f#, there are no IPs there, but #f(0) = 0#, so #(0,0)# is an Infle pt.
