Given function f(x)=x3−3x is a polynomial function.
∴f(x) is continuous as well as differentiable in [−√3,0].
Also, f(−√3)=(−√3)2−3(−√3)=−3√3+3√3=0
And, f(0)=0 Thus, all the three conditions of Rolle's Theorem are satisfied.
∴ There exist at least one real number c, such that f′(c)=0
f′(x)=3x2−3
⇒3c2−3=0
⇒c2=1
⇒c=±1
Thus, c=−1 ∈ (−√3,0)
Hence, value of c is −1.