Determine the Maximum Number of Turning Points of F $$f ( x ) = \left( x + \frac { 1 } { 9 } \right) ^ { 4 } ( x - 4 ) ^ { 3 }$$

question 58

Multiple Choice

Determine the maximum number of turning points of f.
- $$f ( x ) = \left( x + \frac { 1 } { 9 } \right) ^ { 4 } ( x - 4 ) ^ { 3 }$$

• A) above the \(x\)-axis: \(( 4 , \infty )\)
• below the \(x\)-axis: \(\left( - \infty , - \frac { 1 } { 9 } \right) , \left( - \frac { 1 } { 9 } , 4 \right)\)
• B) above the \(x\)-axis: \(\left( - \infty , - \frac { 1 } { 9 } \right) , \left( - \frac { 1 } { 9 } , 4 \right)\)
• below the \(x\)-axis: \(( 4 , \infty )\)
• C) above the \(x\)-axis: \(\left( - \frac { 1 } { 9 } , 4 \right)\)
• below the \(x\)-axis: \(\left( - \infty , - \frac { 1 } { 9 } \right) , ( 4 , \infty )\)
• D) above the x-axis: \(\left( - \infty , - \frac { 1 } { 9 } \right) , ( 4 , \infty )\)
• below the \(x\)-axis: \(\left( - \frac { 1 } { 9 } , 4 \right)\)

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