Question
Question: Let f(x) = 2x<sup>3</sup>+ ax<sup>2</sup> + bx – 3cos<sup>2</sup>x is an increasing function for all...
Let f(x) = 2x3+ ax2 + bx – 3cos2x is an increasing function for all x Î R, then
A
a2 – 6b – 18 > 0
B
a2 – 6b + 18 < 0
C
a2 – 3b – 6 < 0
D
a > 0, b > 0
Answer
a2 – 6b + 18 < 0
Explanation
Solution
f(x) = 2x3 + ax2 + bx – 3cos2x
f '(x) = 6x2 + 2ax + b + 3 sin 2x > 0
6x2 + 2ax + b – 3 > 0 as sin 2x ³ – 1
\ 4a2 – 4b(b – 3) < 0 ̃ a2 – 6b + 18 < 0