Analysis and Approaches for IBDP Maths Ebook 1 | Page 172

Your Practice Set – Analysis and Approaches for IBDP Mathematics
57
Paper 1 Section A – Equations of
tangents and normals
Example
�
Let f( x) � 2e x . The line L is the tangent to the curve of f at (0, 2) . Find the equation
of L in the form y �ax � b .
[6]
Solution
f�
( x)
�x
�2(e )( � 1)
A1
�� 2e �x
The slope of L
� f �(0)
(M1) for finding slope
�� 2e �0
�� 2
(A1) for correct value
The equation of L :
y � �2x � b
(M1) for setting equation
2 � �2(0) � b
(A1) for substitution
b � 2
� y� �2x� 2
A1 N3
[6]
Exercise 57
1. Let f ( x) � sin 3x
. The line L is the tangent to the curve of f at ( � , 0) . Find the
equation of L in the form y �ax � b .
[6]
2. Let f ( x)
� e � x . The line L is the normal to the curve of f at (1, e � ) . Find the equation
of L in the form y �ax � b .
[6]
3. Let f ( x)
� e
of L is
3x
. The line L is the tangent to the curve of f at
3
� 2e
k . Find the value of k .
3k
( ke , )
. The y -intercept
[6]
1
4. Let f ( x) � ln x . The line L is the normal to the curve of f at
2
4
y -intercept of L is 2� 2e
k . Find the value of k .
2k
( e , )
k . The
[6]
164
SE Production Limited