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

question 244

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 \(( 1,1 )\) .

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