The value of c in Rolle’s theorem for the function f(x) = ​ x^3 – 3x in the interval [0, √3] is

Question

The value of c in Rolle’s theorem for the function f(x) = x³ – 3x in the interval [0, \(\sqrt{3}\)] is

A. 1

B. -1

C. \(\frac{3}{2}\)

D. \(\frac{1}{3}\)

Answer 1

Correct answer is A.

f(x) = x³ – 3x

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

\(\therefore\) the function is continous on [0, \(\sqrt{3}\) ] and derivable on [0, \(\sqrt{3}\)].

Differentiating the function with respect to x,

f(x) = x³ – 3x

f’(x) = 3x² – 3

\(\therefore\) f’(c) = 3c² – 3

\(\therefore\) f’(c) = 0

3c² – 3 = 0

c² – 1 = 0

c² = 1

c = ± 1

Hence, c = 1 Є [0, \(\sqrt{3}\)], as per the condition of Rolle’s Theorem.

The required value is c = 3.