Apps. and Interpretation for IBDP Maths Ebook 2 | Page 165

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Exercise 43
1 . Let f ( x) 1 9x 3x x
2 3
� � � � .
( a )
Find f�
( x)
.
( b )
Hence , solve the equation f�( x) �
0.
( c )
( i )
Write down f��
( x)
.
[ 2 ]
[ 2 ]
( ii ) Hence , determine the x -coordinate of the local minimum of f .
( iii ) Write down the y -coordinate of the local minimum of f . [ 4 ]
2 . Let
1 x 2
e f ( x)
� .
2
( a )
Find f�
( x)
.
( b )
Hence , solve the equation f�( x) �
0.
It is given that
1 x
2 2 f ��( x) �( x � 1 ) e .
2
( c ) ( i ) Show that the x -coordinate of the local maximum of f is 0 .
[ 2 ]
[ 2 ]

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( ii ) Hence , write down the y -coordinate of the local maximum of f . [ 3 ] www . seprodstore . com
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