� Slopes of tangents and normals : 1 . f� ( a)
: Slope of tangent at x� a
2 .
�1 f�( a)
: Slope of normal at x� a
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Applications of Differentiation
� Equations of tangents and normals : 1 . y � f ( a) � f �( a)( x � a)
: Equation of tangent at x� a
2 .
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
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Integration
� Integrals of a function y � f ( x) :
1 . � f ( x) dx : Indefinite integral of f( x ) b
2 . � f ( x ) d x : Definite integral of f( x ) from a to b a www . seprodstore . com
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