_{f(x) = x}³ – 3x

_{The above mentioned polynomial function is continuous and derivable in R.}

the function is continous on [0, ] and derivable on [0, ].

Differentiating the function with respect to x,

_{f(x) = x}³ – 3x

_{f’(x) = 3x}² – 3

f’(c) = 3c² – 3

f’(c) = 0

3c² – 3 = 0

c² – 1 = 0

c² = 1

c = ± 1

Hence, c = 1 Є [0, ], as per the condition of Rolle’s Theorem.

The required value is c = 3.

Hence, Option (A) is the answer.