Question
Question: The function f(x) = x<sup>3</sup> + 6x<sup>2</sup>+(9 + 2k)x + 1 is strictly increasing for all x if...
The function f(x) = x3 + 6x2+(9 + 2k)x + 1 is strictly increasing for all x if
A
k ³ 3/2
B
k > 3/2
C
k < 3/2
D
k ³ 3/2
Answer
k > 3/2
Explanation
Solution
f(x) = x3 + 6x2 + (9 + 2k) x + 1
\ f(x) is \ f '(x) > 0
̃ 3x2 + 12x + 9 + 2k > 0
Q x Î R \ D < 0
144 – 4 × 3 (9 + 2k) < 0
12 – 9 – 2k < 0
3 – 2k < 0
k > 3/2