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Calculus, MET1 2022 VCAA 8

Part of the graph of is shown below. The rule gives the area bounded by the graph of , the horizontal axis and the line .
 

  1. State the value of .   (1 mark)

  2. Evaluate .   (2 marks)

  3. Consider the average value of the function over the interval , where .
  4. Find the value of that results in the maximum average value.   (2 marks)

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a.   

b.   

c.   

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a.   
   
   
b.    
 
   
 
   
   
   

♦♦♦ Mean mark (b) 25%.
MARKER’S COMMENT: Common error was giving derivative of as .
c.   Average value  
   
   
   

 
Average value has a maximum value of 1 when


♦♦♦ Mean mark (c) 25%.
MARKER’S COMMENT: Students often chose unnecessarily complicated methods or inconsistently applied nomenclature when attempting this question.