Apps. and Interpretation for IBDP Maths Ebook 1 | Page 197

53
Paper 1 – Gradients of Tangents and Normals
Example
Consider the function
2
f ( x) � 2x �3x
� 4 .
(a) Find the expression of f� ( x)
.
(b) Find the gradient of the graph of f( x ) at x � 5.
(c) Find the gradient of the normal to f( x ) at x �� 5.
[2]
[2]
[2]
15
Solution
(a) f �( x) � 2(2 x) �3(1) � 0
(A1) for correct derivatives
(b)
(c)
Exercise 53
f �( x) �4x
� 3
A1 N2
The gradient
�4(5) � 3
(A1) for substitution
� 23
A1 N2
The gradient of the normal
�1
�
4( �5) �3
(A1) for substitution
1
� A1 N2
17
[2]
[2]
[2]
1. Consider the function
f ( x) �3x � x .
2
4 1
(a) Find the expression of f� ( x)
.
(b) Find the gradient of the graph of f( x ) at x � 0 .
(c) Find the gradient of the normal to f( x ) at x �� 1.
[2]
[2]
[2]
www.seprodstore.com
187