Determine Whether Rolle's Theorem Can Be Applied to the Function $f ( x ) = x ^ { 2 } - 2 x - 3$

Multiple Choice

Determine whether Rolle's Theorem can be applied to the function $f ( x ) = x ^ { 2 } - 2 x - 3$ on the closed interval $( - 1,3 )$ . If Rolle's Theorem can be applied, find all values of $c$ in the open interval $( - 1,3 )$ such that $f ^ { t } ( c ) = 0$ .

A) Rolle's Theorem applies; $c = 1$
B) Rolle's Theorem applies; $\mathrm { c } = 2$
C) Rolle's Theorem applies; $c = 0$
D) Rolle's Theorem applies; $c = - 1$
E) Rolle's Theorem does not apply