3 . The function f is defined as f x � �x � x � x � for x � 2 .
3 2
( ) 13 40 36
( a ) Write down
( i ) the coordinates of the maximum point of f( x );
( ii ) the range of values of x such that f( x ) is increasing .
( b ) ( i ) Find f� ( x) .
[ 4 ]
( ii ) Write down f � ( 5 ) .
( iii ) Hence , show that the equation of the tangent to the graph of f at x � 5 is 15x� y�39 � 0 .
[ 6 ] f( x) � 0 for 2 �x� p. Let R be the region enclosed by the graph of f and the x -axis .
( c ) ( i ) Write down the value of p .
( ii ) Write down the integral representing the area of R .
( iii ) Hence , find the exact value of the area of R . [ 4 ]
( d ) Use the trapezoidal rule with 4 intervals , find an estimate of the area of
R . [ 4 ]
( e ) State whether the estimate in ( d ) overestimates or underestimates
8
� f ( x ) dx .
0
[ 1 ]
© SE Production Limited 10 All Rights Reserved 2021