Determine whether Rolle's Theorem can be applied to $f ( x ) = \frac { x ^ { 2 } - 13 } { x } \text { on the closed }$ interval $[ - 13,13 ]$. If Rolle's Theorem can be applied, find all values of $c$ in the open interval $( - 13,13 )$ such that $f ^ {t } ( c ) = 0$
A) $c = 8$
B) $c = 12 , c = 11$
C) $c = 11 , c = 8$
D) $c = 12$
E) Rolle's Theorem does not apply

Question

Quizplus · Accepted Answer

Rolle's Theorem requires the function to be continuous on the closed interval and differentiable on the open interval. The function $f(x) = \frac{x^2 - 13}{x}$ is not defined at $x = 0$, which lies within the interval $[-13, 13]$, thus violating the continuity requirement. Therefore, Rolle's Theorem does not apply.

Determine Whether Rolle's Theorem Can Be Applied To f(x)=x2−13x on the closed f ( x ) = \frac { x ^ { 2 } - 13 } { x } \text { on the closed }f(x)=xx2−13​ on the closed

Determine Whether Rolle's Theorem Can Be Applied To $f ( x ) = \frac { x ^ { 2 } - 13 } { x } \text { on the closed }$