MonotonicityHard
Question
Function f (x) = x3 + 6x2 + (9 +2k) x + 1 is increasing function if
Options
A.k ≥ 
B.k >
C.k <
D.k ≤
Solution
f (x) = x3 + 6x2 + (9 + 2k)x + 1
f′(x) =3x2 +12x + (9 + 2k)
⇒ 3x2 +12x + (9 + 2k) ≥ 0 ∀ x ∈ R ⇒ D ≤ 0
⇒ 12.12 -12(9 + 2k) ≤ 0
3 - 2k ≤ 0 ⇒ k ≥
.
f′(x) =3x2 +12x + (9 + 2k)
⇒ 3x2 +12x + (9 + 2k) ≥ 0 ∀ x ∈ R ⇒ D ≤ 0
⇒ 12.12 -12(9 + 2k) ≤ 0
3 - 2k ≤ 0 ⇒ k ≥
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