Your Practice Set – Applications and Interpretation for IBDP Mathematics
The point P ( a, f ( a )) , where a � 0 , lies on the graph of f . The tangent at P crosses the
x -axis at the point Q ( 1 , 0 ) .
( a ) ( i ) Find two different expressions of f� ( a) .
( ii ) Hence , find a .
( iii ) Find the equation of [ PQ ] in the form y �mx � c .
( b ) Find the area between the graph of f , the tangent at P and the x -axis .
[ 8 ]
[ 4 ]
3 . Let f ( x)
1 2
� x . The following diagram shows part of the graph of f .
The point A ( h, f ( h )) , where h � 0 , lies on the graph of f . The tangent at A crosses the
x -axis at the point B ( b , 0 ) .
( a ) Express f� ( h) in terms of h .
[ 2 ]
It is given that the gradient of the tangent at A is 1 6 .
( b ) ( i ) Find h .
( ii ) Hence , find the equation of [ AB ] in the form y �mx � c .
( iii ) Find b .
( c ) Find the area between the graph of f , the tangent at A and the x -axis .
[ 6 ]
[ 4 ]
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