Given the polynomial function f(x), find the rational zeros, then the other zeros (that is, solve the equation f(x) = 0), and
factor f(x) into linear factors.
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f ( x ) = \frac { 1 } { 2 } x ^ { 3 } - \frac { 2 } { 3 } x ^ { 2 } - \frac { 1 } { 12 } x + \frac { 1 } { 12 }

\frac { 1 } { 3 } , \frac { 1 + \sqrt { 3 } } { 2 } , \frac { 1 - \sqrt { 3 } } { 2 } ; f ( x ) = \left( x - \frac { 1 } { 3 } \right) \left( x - \frac { 1 + \sqrt { 3 } } { 2 } \right) \left( x - \frac { 1 - \sqrt { 3 } } { 2 } \right)

\frac { 1 } { 2 } , \frac { 1 + \sqrt { 3 } } { 2 } , \frac { 1 - \sqrt { 3 } } { 2 } ; f ( x ) = \left( \frac { 1 } { 3 } \right) \left( x - \frac { 1 } { 3 } \right) \left( x - \frac { 1 + \sqrt { 3 } } { 2 } \right) \left( x - \frac { 1 - \sqrt { 3 } } { 2 } \right)

\frac { 1 } { 2 } , \frac { 1 + \sqrt { 2 } } { 2 } , \frac { 1 - \sqrt { 2 } } { 2 } ; f ( x ) = \left( x - \frac { 1 } { 2 } \right) \left( x - \frac { 1 + \sqrt { 2 } } { 2 } \right) \left( x - \frac { 1 - \sqrt { 2 } } { 2 } \right)

\frac { 1 } { 3 } , \frac { 1 + \sqrt { 3 } } { 2 } , \frac { 1 - \sqrt { 3 } } { 2 } ; f ( x ) = \left( \frac { 1 } { 2 } \right) \left( x - \frac { 1 } { 3 } \right) \left( x - \frac { 1 + \sqrt { 3 } } { 2 } \right) \left( x - \frac { 1 - \sqrt { 3 } } { 2 } \right)

List the Critical Values of the Related Function 2x2+1≥44x2+3\frac { 2 } { x ^ { 2 } + 1 } \geq \frac { 4 } { 4 x ^ { 2 } + 3 }x2+12​≥4x2+34​

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List the Critical Values of the Related Function $\frac { 2 } { x ^ { 2 } + 1 } \geq \frac { 4 } { 4 x ^ { 2 } + 3 }$

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