Could someone verify if I did this right.
f’(x)= -3x^2+6x+9
f’’(x)= -6x+6
0= -6(x-1)
x=1
f’(1)=12
therefore the max slope is 12
You have not justified the claim that this is a maximum, you have just
found a stationary point for the slope.
If f'''(1)<0, then this point will be a maximum for the slope
f'''(1)<0 then it is a minimum
f'''(1)=0 it is indeterminate and further work will be needed.
RonL