Published by:
CGP EDU Academic Team
Published on: August 12, 2026
If p, q, r be real, then the intervals in which, f(x) = 
,
A
increase is x < – 
(p 2 + q 2 + r 2 ), x > 0
(p 2 + q 2 + r 2 ), x > 0
B
decrease is (– 
(p 2 + q 2 + r 2 ), 0)
(p 2 + q 2 + r 2 ), 0)
C
decrease is x < – 
(p 2 + q 2 + r 2 ), x > 0
(p 2 + q 2 + r 2 ), x > 0
D
increase is (– 
(p 2 + q 2 + r 2 ), 0)
(p 2 + q 2 + r 2 ), 0)
Text Solution
Verified by ExpertsThe correct answer is:
CHECK THE SOLUTION.
(a,b)f(x) = 
= x 3 + (p 2 + r 2 + q 2 ) x 2
f ′ (x) = 3x 2 + 2x(p 2 + q 2 + r 2 ) = x {3x + 2(p 2 + q 2 + r 2 )}
Here f(x) is increasing if
x < – 
(p 2 + q 2 + r 2 ) and x > 0
decreasing is if –(p 2 + q 2 + r 2 ) <x < 0
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