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Algebra
Question

For the function \( f ( x ) = ( x - 3 ) ^ { 2 } ( ...

For the function \( f ( x ) = ( x - 3 ) ^ { 2 } ( 4 x - 1 ) \) : a) Find the \( x \) -intercepts and the sign of \( f ( x ) \) before, between, and after the intercepts. b) Determine the location and nature of any stationary points 

Answer

\(x \) - axis interception points of \( ( x - 3 ) ^ { 2 } ( 4 x - 1 ) : ( 3,0 ) , ( \frac { 1 } { 4 } , 0 ) \) 

\( y \) - axis interception point of \( ( x - 3 ) ^ { 2 } ( 4 x - 1 ) : ( 0 , - 9 ) \) 

\( X \) Intercepts: \( ( 3,0 ) , ( \frac { 1 } { 4 } , 0 ) , Y \) Intercepts: \( ( 0 , - 9 )\) 

Solution
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