MonotonicityHard
Question
Function f(x) = x3 + 6x2 + (9 + 2k)x + 1 is increasing function if-
Options
A.k ≥ 3/2
B.k > 3/2
C.k < 3/2
D.k ≤ 3/2
Solution
f(x) = x3 + 6x2 + (9 + 2k) x + 1
f′(x) ≥ 0
f′(x) = 3x2 + 12x + 9 + 2k ≥ 0
D ≤ 0
(12)2 - 4 × 3 (9 + 2k) ≤ 0 12 - 9 - 2k ≤ 0
3 - 2k ≤ 0 3 ≤ 2k
Create a free account to view solution
View Solution FreeMore Monotonicity Questions
Function f(x) = is increasing when...In which of the following intervals f(x) = 2x3 - 15x2 + 36x + 1 is monotonic decreasing -...When x < 0, function f (x) = x2 is...f(x) > x ; ∀ x ∈ R. then the equation f (f(x)) - x = 0 has -...For the function f(x) = x3 − 6x2 − 36x + 7 which of the following statement is false...