For the function, find all points of inflection or determine that no such points exist.

Answer

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.