3 . The function f is defined as f x � � x � x � , 0�x
� 8.
2
( ) 0.25 2 4
( a ) Write down
( i ) the coordinates of the vertex ;
( ii ) the range of f( x ).
( b ) Find f� ( x) .
[ 2 ]
P is a point of the graph of f such that the slope of tangent to the graph of f at P is � 1.
( c ) Show that the coordinates of P are ( 6 , 7 ) . [ 4 ]
( d ) Hence , find the equation of the tangent to the graph of f at P , giving the answer in the form Ax � By �C
� 0 . [ 2 ]
The following table shows the functional values of f( x ) from x � 0 to x � 8:
[ 4 ]
x |
0 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
f( x ) |
f
( 0 )
|
f
( 1 )
|
7 |
7.75 |
8 |
7.75 |
7 |
5.75 |
4 |
( e ) Write down
( i ) f ( 0 );
( ii ) f ( 1 ) .
( f ) Hence , use the trapezoidal rule with 8 intervals , find an estimate for
8
� f ( x ) dx .
0
It is given that the exact value of
8
� f ( x ) dx is 160
0
( g ) State whether the estimate in ( f ) overestimates or underestimates
8
� f ( x ) dx .
0
3 .
[ 2 ]
[ 3 ]
[ 1 ]
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