Paper 1 – Equations of Tangents and Normals

Example

�

Let f( x) � 2e ^x .

( a ) Find f� ( x) .

( b ) ( i ) Find the gradient of the tangent to the curve of f at ( 0 , 2 ) .

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( ii ) Hence , find the equation of the tangent to the curve of f at ( 0 , 2 ) , giving the answer in the form y �ax � b .

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Solution

�x

( a ) f�( x) �2 ( e )( � 1 ) ( M1 ) for chain rule

� f�( x) �� 2e ^x A1

( ii ) The equation of the tangent : y � �2x � b ( M1 ) for setting equation

2 � �2 ( 0 ) � b

( M1 ) for substitution b � 2 � y� �2x� 2 A1

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