The function f ( x ) = a x 3 + b x 2 + c x + d has its non-zero local minimum and maximum values at x = − 2 and x = 2 respectively if ' a ' is root of x 2 − x − 6 = 0 then List - I List -

Question

The function f ( x ) = a x 3 + b x 2 + c x + d ​ has its non-zero local minimum and maximum values at x = − 2 and x = 2 respectively if ' a ' is root of x 2 − x − 6 = 0 then List - I List - II (A) The value(s) of ˋa' is (are) (p) 0 (B) Value(s) of 'b' is (are) (q) 24 (C) Value(s) of 'c' is (are) (r) > 32 (D) Value(s) of 'd' is (are) (s) -2

TestHub · Accepted Answer

a < 0 ⇒ a = − 2 , then g ( x ) = − 2 x 3 + 6 x 2 + cx + d ; g ′ ( x ) = − 6 ( x + 2 ) ( x − 2 ) ⇒ b = 0 , c = 24 , also d > 32 which can be evaluated by f ( − 2 ) = − 8 a + 4 b − 2 c + d ​

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JEE Advanced 2027 (Class 12+)

List - I	List - II
(A) The value(s) of ˋa' is (are)	(p) 0
(B) Value(s) of 'b' is (are)	(q) 24
(C) Value(s) of 'c' is (are)	(r) > 32
(D) Value(s) of 'd' is (are)	(s) -2