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Calculus, 2ADV C3 2019 HSC 14b

The derivative of a function    is given by  .

  1. Find the -values of the two stationary points of  , and determine the nature of the stationary points.  (2 marks)

  2. The curve passes through the point  .

     

    Find an expression for  .  (2 marks)

  3. Hence sketch the curve, clearly indicating the stationary points.  (2 marks)

  4. For what values of is the curve concave down?  (1 mark)

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a.   

 


 

 

b.   
   
   

 

 

c.   
 

 

 

d.   

♦ Mean mark 36%.

Calculus, 2ADV C3 2004 HSC 4b

Consider the function  .

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

  2. Sketch the curve showing where it meets the axes.   (2 marks)

  3. Find the values of    for which the curve    is concave up.   (2 marks)

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  2.  
    1. Geometry and Calculus, 2UA 2004 HSC 4b Answer
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(i)   
 
 

 

 

 

 

(ii)  

 Geometry and Calculus, 2UA 2004 HSC 4b Answer

(iii)  

 

Calculus, 2ADV C3 2005 HSC 4b

A function    is defined by  .

  1. Find all solutions of   (2 marks)

  2. Find the coordinates of the turning points of the graph of  , and determine their nature.  (3 marks)

  3. Hence sketch the graph of  , showing the turning points and the points where the curve meets the -axis.  (2 marks)

  4. For what values of is the graph of    concave down?  (1 mark)

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i.   
   
 

 

ii.  
   
   
 
 

 

 

 
 

 

 

iii.   Geometry and Calculus, 2UA 2005 HSC 4b Answer

 

iv. 

Calculus, 2ADV C3 2010 HSC 6a

Let  .

  1. Show that the graph    has no stationary points.   (2 marks)

  2. Find the values of    for which the graph    is concave down, and the values for which it is concave up.    (2 marks)

  3. Sketch the graph  ,  indicating the values of the    and   intercepts.   (2 marks)

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  2.  

     

  3.  
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i. 

 

 

 
 
 

 

 

ii. 

MARKER’S COMMENT: The significance of the sign of the second derivative was not well understood by most students.

 

♦♦ Mean mark 33%.
MARKER’S COMMENT: Students are reminded to bring a ruler to the exam and use it to draw the axes for graphing and to help with an appropriate scale.

iii.