Question
Question: If f(x) = (a + 2)x<sup>3</sup> – 3ax<sup>2</sup> + 9ax – 1 is decreasing on R, then 'a' lies in the ...
If f(x) = (a + 2)x3 – 3ax2 + 9ax – 1 is decreasing on R, then 'a' lies in the interval-
A
(–¥, – 2)
B
(–2, ¥)
C
(–3, 0)
D
(– ¥, –3]
Answer
(– ¥, –3]
Explanation
Solution
Q f(x) is decreasing function
\ f ¢(x) £ 0
̃ 3(a + 2)x2 – 6ax + 9a £ 0
̃ (a + 2)x2 – 2ax + 3a £ 0
̃ a + 2 < 0 and D £ 0
̃ a < – 2 and 4a2 – 12a(a + 2) £ 0
a < – 2 and –8a2 – 24a £ 0
̃ a < – 2 and a(a + 3) ³ 0
a < – 2 and a £ – 3 or a ³ 0
̃ a £ –3 ̃ – ¥ < a £ –3