Your Practice Paper – Analysis and Approaches HL for IBDP Mathematics
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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
� Properties of rate of change : d d d
1 . N � N � x dt dx dt dy dy 2 . � dt dx dx dt
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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
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