Question
Question: Let f(x) = x<sup>3</sup> + 6x<sup>2</sup> + px + 2. If the largest possible interval, in which f(x) ...
Let f(x) = x3 + 6x2 + px + 2. If the largest possible interval, in which f(x) is a decreasing function, is (–3, –1), then p equals
A
9
B
3
C
–2
D
None of these
Answer
9
Explanation
Solution
f ¢(x) = 3x2 + 12x + p < 0
Q f(x) is decreasing in (– 3, – 1)
̃ f ¢(x) £ 0 in (– 3, – 1)
̃ 3 × (–3)2 + 12 × (–3) + p £ 0 and
3 × (–1)2 + 12 × (–1) + p £ 0 ̃ p £ 9 ̃ p = 9