Verify That the Function Satisfies the Three Hypotheses of Rolle's $f(x)=x^{3}-5 x^{2}+6 x+2,[0,4]$

Multiple Choice

Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval. Then find all numbers c that satisfy the conclusion of Rolle's Theorem. $f(x) =x^{3}-5 x^{2}+6 x+2,[0,4]$

A) $c=2-\frac{2 \sqrt{3}}{3}$
B) $c=2+\frac{2 \sqrt{3}}{3}$
C) $c_{1}=12+\frac{\sqrt{2}}{3}, c_{2}=12-\frac{\sqrt{2}}{3}$
D) $c_{1}=\frac{5}{3}+\frac{\sqrt{7}}{3}, c_{2}=\frac{5}{3}-\frac{\sqrt{7}}{3}$
E) $c_{1}=2+\frac{2 \sqrt{3}}{3}, c_{2}=\frac{2 \sqrt{3}}{3}$