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Calculus, 2ADV C3 2017 HSC 13b

Consider the curve  .

  1. Find the stationary points of the curve and determine their nature.  (4 marks)

  2. Sketch the curve, labelling the stationary points.  (2 marks)

  3. Hence, or otherwise, find the values of for which is positive.  (1 mark)

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Calculus, 2ADV C3 2012 HSC 14a

A function is given by  . 

  1. Find the coordinates of the stationary points of    and determine their nature.   (3 marks)

  2. Hence, sketch the graph     showing the stationary points.   (2 marks)

  3. For what values of    is the function increasing?   (1 mark)

  4. For what values of    will    have no solution?   (1 mark)

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        2UA HSC 2012 14ai
     
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ii.  2UA HSC 2012 14ai
♦ Mean mark 42%
MARKER’S COMMENT: Be careful to use the correct inequality signs, and not carelessly include ≥ or ≤ by mistake.

 

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♦♦♦ Mean mark 12%.