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Calculus, 2ADV C1 2010 HSC 7b

The parabola shown in the diagram is the graph  . The points    and    are on the parabola.
 

 
 

  1.  Find the equation of the tangent to the parabola at .   (2 marks)

  2.  Let be the midpoint of  .

     

    There is a point on the parabola such that the tangent at is parallel to  .

     

    Show that the line    is vertical.   (2 marks)  

  3. The tangent at meets the line at .

     

    Show that the line is a tangent to the parabola.  (2 marks)

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i.
 

 

 

 

 

 

♦ Mean mark 37%.
IMPORTANT: The critical understanding required for this question is that the gradient of needs to be equated to the gradient function (i.e. ).

ii.   

 

 

 

 

 

 

 

 

iii.    

♦♦ Mean mark 29%.

 

 

 

Calculus, 2ADV C1 2011 HSC 2c

Find the equation of the tangent to the curve     at the point where  .   (3 marks)

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MARKER’S COMMENT: The best setting out clearly showed the derivative function, the gradient, the point and then finally, calculations for the equation of the tangent, as per the Worked Solution.