Use the Function Below and Its Derivative to Determine Any $f$

Multiple Choice

Use the function below and its derivative to determine any points on the graph of $f$ at which the tangent line is horizontal.
$$f ( x ) = - 2 x ^ { 4 } + 4 x ^ { 2 } , \quad f ^ { \prime } ( x ) = - 8 x ^ { 3 } + 8 x$$

A) $( - 1,2 ) , ( 0,0 ) , ( 1,2 )$
B) $( - 1 , - 2 ) , ( 1 , - 8 )$
C) $( - 1,2 ) , ( 1,2 )$
D) $( 0,0 ) , ( 1,0 )$
E) $( 0,0 ) , ( 1,2 )$