Apps. and Interpretation for IBDP Maths Ebook 1 | Page 195

Chapter
15
15
Differentiation
SUMMARY POINTs
�
�
�
dy
� f�( x)
: Derivative of the function y � f ( x)
(First derivative)
dx
Rules of differentiation:
1.
n
f ( x) � x � f �( x)
� nx �
n 1
2. f ( x) � p( x) � q( x) � f �( x) � p�( x) � q�( x)
3. f ( x) �cp( x) � f �( x) � cp�( x)
Relationship between graph properties and the derivatives:
1. f�( x) � 0 for a �x � b : f( x ) is increasing in the interval
2. f�( x) � 0 for a �x � b : f( x ) is decreasing in the interval
3. f�( a) � 0: ( a, f ( a )) is a stationary point of f( x )
4. f�( a) � 0 and f� ( x)
changes from positive to negative at x� a:
( a, f ( a )) is a maximum point of f( x )
5. f�( a) � 0 and f� ( x)
changes from negative to positive at x� a:
( a, f ( a )) is a minimum point of f( x )
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