4 . Let f ( x)
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� . The following diagram shows part of the graph of f . x
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The point A ( h, f ( h )) , where h � 0 , lies on the graph of f . The normal at A crosses the
x -axis at the point B ( b , 0 ) .
( a ) Express f� ( h) in terms of h .
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It is given that the gradient of the tangent at A is 3 4 .
( b ) ( i ) Find h .
( ii ) Write down the gradient of the normal at A .
( iii ) Hence , find the equation of [ AB ] in the form y �mx � c .
( iv ) Find b .
( c ) Find the area between the graph of f , the normal at A and the x -axis .
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