Mark the correct alternative in the following:

The value of e in Rolle’s theorem show f(x) = 2x3 – 5x2 – 4x + 3, is x ϵ[1/3, 3]


f(x) = 2x3 – 5x2 – 4x + 3


f’(x) = 6x2 – 10x – 4


f’(c) = 6c2 – 10c – 4


f’(c) = 0


6c2 – 10c – 4 = 0


3c2 – 5c – 2 = 0


3c2 + c – 6c – 2 = 0


c (3c + 1) – 2 (3c + 1) = 0


(3c + 1) (c – 2) = 0


c = 2 or


c = 2 Є


Thus, as per Rolle’s Theorem, c = 2 Є .


So, the required value of c = 2


Hence, Option (A) is the answer.

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