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Does f(x)=x3−2x2+1f ( x ) = x ^ { 3 } - 2 x ^ { 2 } + 1

Question 48

Essay

Does f(x)=x3−2x2+1f ( x ) = x ^ { 3 } - 2 x ^ { 2 } + 1 satisfy the hypothesis of the Mean Value Theorem on the interval [0,3]. If it does, then find the exact values of all c∈(0,3)c \in ( 0,3 ) that satisfy the conclusion of the Mean Value Theorem.

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