Your Practice Paper – Applications and Interpretation HL for IBDP Mathematics

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

� 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 )

� Tangents and normals : 1 . f� ( a)

: Slope of tangent at x� a

2 .

�1 f�( a)

: Slope of normal at x� a

3 . y � f ( a) � f �( a)( x � a) : Equation of tangent at x� a

4 . ^{y f} 1 ( ^a � � �

� ) � � ( ) f ( a) ^x � �

� ^a � �

� Derivatives of a function y � f ( x)

:

1 .

2 .

2 d y d �d �

2 � d d d

y�

�� x x � x � n d y n dx

: Equation of normal at x� a f��( x) : Second derivative

( n) � f ( x)

: n -th derivative

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