Question

find the inflection point of
y=x^3-6x^2+9+4

Answer 1

y' = 3x^2 - 12x + 9 (i think u meant 9x, not just 9)
y" = 6x - 12

Answer 2

Now set y" = 0 and see if the concavity changes when y" = 0:
6x - 12 = 0
6x = 12
x = 2

Answer 3

All we gotta do now is check if concavity changes:

See the signs changed. The easy way to test this was picking something in the interval from (-inf, 2) I picked 0 to test, because it was easy.