Analysis and Approaches for IBDP Maths Ebook 2 | Page 140

Your Practice Set – Analysis and Approaches for IBDP Mathematics
Exercise 43
1. Find the gradient of the curve
e .
2 y
x � y � e ln x � 2 at (1,1) , giving the answer in terms of
[6]
2. Find the coordinates of the points on the curve
� � � � at which d y
0
dx [8]
2 2
( x 3) 4y 4(4y
3)
3. Let
xy
2
� � . Using implicit differentiation to show that
y
3
2
d y dy xy
( x� 2 y) � � � 0 .
2 2
dx d x ( x � 2 y)
x y
4. Let e � e � 4x
� 0. Using implicit differentiation to show that
2
2y d y
x 2 x�
y
e � (4 � e ) � e � 0 .
2
dx
[7]
[6]
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