Question

2x³ + 18x² - 96x + 45 = 0 is an increasing function when 

(A) x ≤ - 8, x ≥ 2 

(B) x < - 2, x ≥ 8 

(C) x ≤ − 2, x ≤ 8

(D) 0 ≤ x ≤ - 2

Answer 1

Answer is (A) x ≤ - 8, x ≥ 2

We have f'(x) = 6x² + 36x - 96 > 0

for increasing function

f'(x) = (x + 8) (x - 2) ≥ 0

⇒ x ≥ 2, x ≤− 8