Apps. and Interpretation for IBDP Maths Ebook 1 | Page 199

54
Paper 1 – Equations of Tangents and Normals
Example
Let
3
f ( x) � 2 � x � . The line L is the tangent to the curve of f at (1, 0) .
x
(a) Find the expression of f� ( x)
.
(b) Find the gradient of L .
(c) Find the equation of L in the form y �ax � b .
[2]
[2]
[2]
15
Solution
(a)
(b)
f � x � � � � x �
(A1) for correct derivatives
2
( ) 0 1 3( )
2
� � � A1 N2
f ( x) 1 3x �
The gradient of L
�1� 3(1) �2
(A1) for substitution
� 4
A1 N2
(c) The equation of L :
y�0 � 4( x� 1)
(A1) for substitution
y�4x� 4
A1 N2
[2]
[2]
[2]
Exercise 54
1. Let
f ( x) 6x 21x
4 2
� � . The line L is the tangent to the curve of f at (2,12) .
(a) Find the expression of f� ( x)
.
(b) Find the gradient of L .
(c) Find the equation of L in the form y �ax � b .
[2]
[2]
[2]
www.seprodstore.com
189