Published by:
CGP EDU Academic Team
Published on: August 14, 2026
If all the extreme value of function f(x) = a 2 x 3 – 
x 2 – 2x – b are positive and the minimum is at the point x 0 = 
then show that when a = –2 ⇒ b < 
and when a = 3 ⇒ b < – 
Text Solution
Verified by ExpertsThe correct answer is:
CHECK THE SOLUTION.
f’(x) = 0 ⇒ x = 
, 
since, we have a cubic polynomial with coefficient of x 3 +ve , minima will occur after maxima.
Case - 1 : If a > 0
then 
= 
⇒ a = 3
also f 
> 0 ⇒ b < – 
Case - 2 : If a < 0
then – 
= 
⇒ a = – 2
also f 
> 0 ⇒ 
– 
. 
– 2 
– b > 0 ⇒ 
⇒ b < 
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