MonotonicityMedium

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

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