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.
