Here was the whole question: f(x)=-x^3+13.5x^2-800

A.) Find the critical values and create a sign diagram for the first derivative. f'(x)=-3x^2+27x

(-infinity,0), (0,9), (9,infinity) with the sign diagram going neg to pos to neg with a relative max of 9 at -435.5 and a relative min. of 0 at -800.

The next part is what I am not sure of how to do. I know the second derivative is -6x+27 and I set that equal to 0 and got x=4.5. So now what do I do? After that the question is identify any inflection points of the function. Then Create a well labeled sketch of the function. Any help would be very appreciated! I am taking this class for the second time and starting to understand it but still have trouble putting it all together!!