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

Multiple Choice

Use the function and its derivative to determine any points on the graph of $f$ at which the tangent line is horizontal.Use a graphing utility to verify your results. $f ( x ) = 5 x ^ { 6 } + 6 x ^ { 5 } , \quad f ^ { \prime } ( x ) = 30 x ^ { 5 } + 30 x ^ { 4 }$

A) $f$ has vertical tangents at $( - 1 , - 1 )$ and $( 0,0 )$ .
B) $f$ has horizontal tangents at $( 1,1 )$ and $( 0,0 )$ .
C) $f$ has horizontal tangents at $( - 1 , - 1 )$ and $( 0,0 )$ .
D) $f$ has vertical tangents at $( 1,1 )$ and $( 0,0 )$ .
E) $f$ has vertical tangents at $( - 1 , - 1 )$ and $( 1,1 )$ .