3 . The function f is given by that the local minimum point is located at x � 8.
3 2 f ( x) � �x �bx � 432x
� 2456 , b , x� . It is given
( a ) Find b .
( b ) Hence , write down
[ 4 ]
( i ) the y -coordinate of the local minimum ;
( ii ) the coordinates of the local maximum .
( c ) Write down the range of values of x such that f is increasing .
( d ) Write down the range of values of k such that the equation f ( x) has
� k
[ 3 ]
[ 2 ]
( i ) three solutions ;
( ii ) at most two solutions .
[ 4 ] The average cost Cx ( ) dollars of producing x thousands smart watches in a
company can be modelled by the function 0 �x
� 25.
3 2
C( x) � �x �bx � 432x
� 2456 ,
( e ) Show that the average cost attains its minimum when 25000 smart watches are produced .
[ 2 ] ( f ) Find the range of values of x such that the average cost is not greater than $ 984 . [ 3 ]
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