Answer 1

f(x)  = 4x³ - 6x² - 72x + 30 

f'(x) = 12 x²  - 12x - 72

(a) For strictly increasing funciton

f;(x) > 0

12x² - 12x - 72 >0

x² - x - 6 > 0 .

x²  - 3x +2x - 6>0 

(x - 3) (x + 2) > 0

⇒ x ∈ (-∞ , - 2) ∪ (3 , ∞)

(b) For strictly decreasing function 

f '(x) < 0

12 x² - 12x - 72 < 0

x²  - x-6 < 0

(x + 2 ) (x - 3) < 0

⇒ x ∈ ( -2 , 3 )