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

question 108

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) \(c_{1}=2+\frac{2 \sqrt{3}}{3}, c_{2}=\frac{2 \sqrt{3}}{3}\)

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