You have a positive sign on both sides of the critical value, and since the second derivative is a linear function with positive slope, we know it must go from negative to positive across the critical value. You found the correct value, I just wanted you to be aware of the change of sign of the second derivative. In fact, if the sign does not change, then you do not have a point of inflection.
If you are asked for the inflection point, then you need the y-value, so plug the critical number into the oriinal function to get the y-coordinate of the inflection point. What does the sign of the second derivative on either side of the critical value tell you about concavity?