Consider the following function.

f$($x$)=9$ x$^(2/3)$

Find

f$(27)$ and f$(27).$

f$(27)=$

f$(27)=$

Find all values c in $(27,27)$ such that

f$\text{'}($c$)=0.$

$($Enter your answers as a comma$-$separated list. If an answer does not exist, enter DNE.$)$

c $=$

Based off of this information, what conclusions can be made about Rolle's Theorem?

This contradicts Rolle's Theorem, since f is differentiable, f$(27)=$ f$(27),$ and f$\text{'}($c$)=0$ exists, but c is not in $(27,27).$

This does not contradict Rolle's Theorem, since f$\text{'}(0)=0,$ and $0$ is in the interval $(27,27).$

This contradicts Rolle's Theorem, since f$(27)=$ f$(27),$ there should exist a number c in $(27,27)$ such that f$\text{'}($c$)=0.$

This does not contradict Rolle's Theorem, since f$\text{'}(0)$ does not exist, and so f is not differentiable on $(27,27).$

Nothing can be concluded.