For the function, find all points of inflection or determine that no such points exist.
Since f " is a polynomial it is never undefined. Its roots are x = 2 and x = 3:
When x < 2, both x - 2 and x - 3 are negative, so f " is positive:
When x is between 2 and 3, the quantity x - 2 is positive but x - 3 is negative so f " is negative:
Finally, when x is greater than 3 both x - 2 and x - 3 are positive, so f " is positive:
Since the sign of f " changes at x = 2 and x = 3, these are both inflection points.