posted by henry .
defined on the interval [-18,20]
f(x) is concave up on the region ? to ? and ? to ?
the inflection points are ?, ? and ?
I assume you mean f(x) = x^3/(x^2-4)
First find the points where f'(x) = 0
f'(x) = [(x^2-4)(3x^2)-2x^4]/(x^2 -4)^2
(x^2-4)(3x^2)-2x^4 = 0 when f'(x) = 0
3x^4 -12 x^2 -2x^4 = 0
x = 0, +2sqrt3 and -2sqrt3
Now evaluate the second derivative at those three critical points. The function is concave up if f''(x) > 0 and is an inflection point if f''(x) = 0