Your Practice Set – Applications and Interpretation for IBDP Mathematics
Exercise 42
1 . Let f ( x) � sin 3x .
( a ) Find f� ( x) .
( b ) ( i ) Find the gradient of the tangent to the curve of f at ( � , 0 ) .
[ 2 ]
( ii ) Hence , find the equation of the tangent to the curve of f at ( � , 0 ) , giving the answer in the form y �ax � b and in terms of � .
[ 5 ]
2 . Let f ( x) ln x
3
� .
( a ) Find f� ( x) .
( b ) ( i ) Find the gradient of the tangent to the curve of f at ( 1 , 0 ) .
[ 2 ]
( ii ) Hence , write down the gradient of the normal to the curve of f at ( 1 , 0 ) .
( iii ) Find the equation of the normal to the curve of f at ( 1 , 0 ) , giving the answer in the form y �ax � b .
[ 6 ]
3 . Let f ( x)
3x
� e .
( a ) Find f� ( x) .
[ 2 ]
( b ) Hence , write down the gradient of the tangent to the curve of f at giving the answer in terms of k .
It is given that the equation of the tangent to the curve of f at 1
is 3x� y� 2 � 0 .
3 e
3k
( , )
3k
( , )
ke ,
[ 1 ]
ke , where 0 �k � 10 ,
( c ) Find the value of k . [ 3 ]
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