Published by:
CGP EDU Academic Team
Published on: August 14, 2026
The set of all values of the parameters a for which the points of minimum of the function y = 1 + a 2 x – x 3 satisfy the inequality 
≤ 0 is -
A
An empty set
B
C
D
∪ 
Text Solution
Verified by ExpertsThe correct answer is:
C
= a 2 – 3x 2 = 0 ⇔ x = ± a/ 
.
Since 
= –6x so y is minimum for x = –a/ 
.
Since x 2 + x + 2 > 0 for all x so for 
≤ 0,
we must have x 2 + 5x + 6 < 0.
If x = –a/ 
, we have a 2 /3 – 5a/ 
+ 6 < 0 i.e. a 2 – 5 
a + 18 < 0
⇔ (a – 2 
) (a – 3 
) < 0 i.e. a ∈ (2 
, 3 
).
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