Analysis and Approaches for IBDP Maths Ebook 1 | Seite 152

Your Practice Set – Analysis and Approaches for IBDP Mathematics
SUMMARY POINTs
�
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 )
6. f��( a) � 0 and f�� ( x)
changes sign at x� a: ( a, f ( a )) is a point of
inflexion of f( x )
�
Slopes of tangents and normals:
1. f� ( a)
: Slope of tangent at x�
a
2.
�1
f�( a)
: Slope of normal at x�
a
Solutions of Chapter 13
144
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