Your Practice Set – Applications and Interpretation for IBDP Mathematics
Exercise 41
1 . Let f ( x) � 3xcos
x .
( a ) Find f� ( x) .
( b ) ( i ) Find the gradient of the tangent to the curve of f at
3� x � . 2
[ 2 ]
( ii ) Hence , find the gradient of the normal to the curve of f at
3� x � . 2
[ 4 ]
2 . Let f ( x)
� .
3x
e �
( a ) Find f� ( x) .
( b ) ( i ) Find the gradient of the tangent to the curve of f at x � 0.1.
( ii ) Hence , find the gradient of the normal to the curve of f at x � 0.1.
[ 2 ]
[ 4 ]
3 . Let f x
2
( ) cos ( x )
� .
( a ) Find f� ( x) .
The gradient of the tangent to the curve of f at x
� a is � 2a , where 1�a
� 2.
[ 2 ]
( b ) Find a . [ 3 ]
4 . Let
2 g( x) x ln x
� .
( a ) Find g� ( x) .
The gradient of the tangent to the curve of g at x � a is a , a � 0 .
[ 2 ]
( b ) Find a . [ 3 ]
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