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

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: $\left( - \frac { 1 } { 9 } , 4 \right)$