3 . The function f is given by
4 3 2 f ( x) � x � 5x � 6x
� 2 , x� .
3
( a ) Write down the y -intercept of the graph of f .
( b ) Find f ( 3 ) .
( c ) Find f� ( x)
.
( d ) Solve the equation f�( x) � 0.
[ 3 ] ( e ) Write down the equations of the horizontal tangents of the graph of f .
( f ) Write down the range of values of w such that the equation f ( x) has
( i ) three solutions ;
[ 1 ]
[ 2 ]
[ 2 ]
[ 2 ]
� w
( ii ) only one solution .
( g ) Find the gradient of the tangent at x � 3.
( h ) Hence , show that the equation of the normal at x � 3 is x� 60y� 3903 � 0 .
[ 4 ]
[ 2 ]
[ 3 ]
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