Verified answer

f' = 6x^2 - 114x + 540

f' = 6(x^2 - 19x + 90)

0 = (x^2 - 19x + 90)

0 = (x - 10)(x - 9)

x = 10 and x = 9

Those are your critical points.

f'(0) = +

f'(9.5) = -

f'(11) = +

Inteveal that it is decreasing:

[9,10]

A function is decreasing where f'(x) has negative values.

f'(x) = 6x^2 - 114x + 540

6x^2 - 114x + 540 = 0

3x^2 - 57x + 270 = 0

x = (57 +/- 3)/6 = 9, 10

f'(x) < 0 on [9 , 10]