Analysis and Approaches for IBDP Maths Ebook 1 | страница 171

Front Page
Chapter
14
14
Applications of
Differentiation
SUMMARY POINTs
�
�
�
�
Equations of tangents and normals:
1. y � f ( a) � f �( a)( x � a)
: Equation of tangent at x�
a
2.
Rate of change:
1.
y f 1
( a � � �
� ) � � ( )
f ( a)
x �
�
� a
� �
: Equation of normal at x�
a
dN dN dx
� � : Rate of change of N with respect to the time t
dt dx dt
Tests for optimization:
1. First derivative test 2. Second derivative test
Applications in kinematics:
1. st (): Displacement with respect to the time t
2. v( t) � s�( t)
: Velocity 3. a( t) � v�( t)
: Acceleration
Solutions of Chapter 14
www.seprodstore.com
163