Does $f ( x ) = 2 x ^ { 2 } + \frac { 1 } { x }$

True/False

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