8 . A function f has its derivative
2
�( ) � �12 � 40, where k is a constant . f x kx x
( a ) Express f�� ( x) in terms of k and x .
The graph of f has a point of inflexion when x � 1.5.
[ 2 ]
( b ) Show that k � 4 .
( c ) Find the equation of the normal to the curve of f at your answer in the form y �ax � b .
It is given that f �( 5 ) � 0.
� 13 � �4 , � � 6 � , giving
[ 3 ]
[ 6 ]
( d ) Show that the graph of f has a local minimum at x � 5. [ 3 ]
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