Question

Function f(x) = x 3 − 27x + 5 is monotonically increasing when
(a) x < −3
(b) | x | > 3
(c) x ≤ −3
(d) | x | ≥ 3

Answer 1

c answer x< -3 I shore you are

Answer 2

Answer:

| x | ≥ 3

f(x)=x^3−27x+5

f'(x)=3x^2−27 =3 (x^2−9)

For f(x) to be increasing, we must have f'(x)>0⇒3 (x^2−9)>0⇒(x^2−9)>0 [Since 3>0,

3(x^2−9)>0⇒| (x^2−9)>0|]

⇒(x+3)(x−3)>0

⇒x<−3 or x>3⇒|x|>3