Analysis and Approaches for IBDP Maths Ebook 2 | Page 139

43
Paper 1 Section A – Implicit Differentiation
Example
Find the coordinates of the point on the curve
5y 3x 2xy
y � and
2 3
� � at which 1
dy
8
dx �� . [7]
Solution
5y �3x � 2xy
2 3
d d 2 d 3
(5 y) � (3 x ) � (2 xy )
(M1) for valid approach
dx dx dx
dy
3 � 2 dy�
5 � 6 x � (2)( y ) � (2 x) �3y
�
(A2) for correct approach
dx
� dx�
dy
3 2 dy
5 � 6x � 2y � 6xy
dx
dx
dy
2 dy
3
5 � 6xy � 2y � 6x
dx
dx
2 dy
3
(5 � 6 xy ) � 2y � 6x
dx
3
d 2 � 6
y y x
� A1
2
dx
5 � 6xy
3
2(1) � 6
x
� � �8
2
5 � 6 x(1)
(A1) for substitution
2 � 6x� �8(5 � 6 x)
2� 6x� �40 � 48x
(M1) for valid approach
42 � 42x
x � 1
Thus, the required coordinates are (1,1) .
A1
[7]
10
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