find the interval in which the function f given by f(x)=20 - 9 x + 6 x²-x³ is (a) strictly increasing (b) strictly decreasing?

f(x) = 20 - 9x - 6x^​2 - x³ 
f''(x) = - 9 - 12x - 3x2 
for f''(x) = 0
- 9 + 12x - 3x² = 0
x² - 4x + 3 = 0
x = 1,3
now, f'''(x) = 12 - 6x
f'''(1) = 6
f'''(3) = -6
f(x) is strictly increasing at x belongs to (infinity,1) U (3,infinity)
f(x) is strictly decreasing at x belongs to (1,3)