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

question 56

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.
$$f ( x ) = 3 x ^ { 4 } - 6 x ^ { 2 } , f ^ { \prime } ( x ) = 12 x ^ { 3 } - 12 x$$

• A) \(( - 1 , - 3 ) , ( 0,0 ) , ( 1 , - 3 )\)
• B) \(( - 1,3 ) , ( 1,12 )\)
• C) \(( - 1 , - 3 ) , ( 1 , - 3 )\)
• D) \(( 0,0 ) , ( 1,0 )\)
• E) \(( 0,0 ) , ( 1 , - 3 )\)