The exhaustive set of values of 'a' for which the function f(x) = 
x 3 + (a + 2) x 2 + (a − 1) x + 2 possess a negative point of minimum is (q, ∞ ). The value of q is :
Text Solution
Verified by Experts1
(1)
f ′ (x) = ax 2 + 2 (a + 2) x + (a – 1)
case - I a = 0
f ′ (x) = 4x – 1
Minima at x = 
. Not negative
∴ a ∈ φ .... (i)
case - II a ≠ 0
Let g(x) = x 2 + 2 x 
+ 
. g(x) = 0
must have larger root as negative.
g(0) > 0, 
< 0, 
– 4.1. 
> 0
⇒ a ∈ (1, ∞ ) .... (ii)
Union of (i), (ii) is a ∈ (1, ∞ )
──────────────────────────────────────────────────────────────────────────────────────────
Prepare Smarter with CGP Edu
Get practice questions, solutions, and test series in one place.
Write a Review
Share your experience with this question and solution.
Commentary
Send your comment, doubt, correction, or feedback to admin.
Similar Questions
Explore conceptually related problems