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Calculus, 2ADV C3 2020 HSC 29

The diagram shows the graph of  .
 

  1. Show that the equation of the tangent to    at  , where  , is
     
    .  (2 marks)

  2. Find the value of such that the tangent from part (a) has a gradient of 1 and passes through the origin.  (2 marks)

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a.   

 

 

b.   

♦ Mean mark part (b) 40%.

 

 

Calculus, 2ADV C3 2014 HSC 15c

The line    is a tangent to the curve    at a point  . 

  1. Sketch the line and the curve on one diagram.   (1 mark)

  2. Find the coordinates of  .     (3 marks)

  3. Find the value of  .   (1 mark)

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  1.   
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i. 

 

ii.
 

 

♦ Mean mark 40%
COMMENT: Given , it follows . Make sure you understand the arithmetic behind this (NB. Simply take the of both sides).

 

 
 

 

 

iii.   

♦♦ Mean mark 30%.