BBMP1103 - Sept 2011 exam workshop - Part 2

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BBMP1103 - Sept 2011 exam workshop - Part 2

  1. 1. BBMP 1103 Mathematic ManagementExam Preparation Workshop Sept 2011 Part 2 - Differentiation Presented By: Dr Richard Ng 26 Nov 2011 2ptg – 4ptg
  2. 2. 2. Focus on Differentiation Question: 4 (May 2010) Differentiate the following functions: a) f ( x) 5 x3 Find f ( x) and f ( x) 3 marks 2 b) f ( x) x 3 (x6 2 x 3 1) Find f ( x) 3 marks c) f ( x) [( x 3)(4 x 2 2 x)] Find f ( x) 4 marks 5 x 3 3x 2 7 d) p( x) Find p ( x) 3 marks x2Prepared by Dr Richard Ng (2011) Page 2
  3. 3. Suggested Answers: 3 1 a) f ( x) 5 x 15 2 3 f x 2 2 f ( x) 5x 1 1 15 2 1 f x 3 2 2 2 f (5) x 2 1 1 15 15 2 f x 2 f x 2 4Prepared by Dr Richard Ng (2011) Page 3
  4. 4. 2 3 b) f ( x) x (x6 2 x 3 1) 2 1 3 5 2 6 3 2 3 f x 6x 6x (x 2x 1) x 3 c) f ( x) x 3 (4 x 2 2 x) f x 3 8x 2 (4 x 2 2 x) 1 f x 3 8 (8x 2) 1 (8x 2) 8x 24 (8x 2) (8x 2) 24x 28Prepared by Dr Richard Ng (2011) Page 4
  5. 5. 5 x 3 3x 2 7 d) p ( x) x2 5x 3 3x 2 7 x2 x2 x2 2 5x 3 7 x 3 p 5 ( 2)7 x 3 5 14x 4 p 42xPrepared by Dr Richard Ng (2011) Page 5
  6. 6. Question: 5 (January 2011)
  7. 7. a) y 12x 3 442x 2 300x 6 3x 1 d) y dy 5x 2 36x 2 884x 300 dx dy (5 x 2)[3] (3x 1)[5] dx (5 x 2) 2 1 2b) y x x2 15x 6 (15x 5) dy 2x 3 (5 x 2) 2 dx 5 11 x 3x 1 5 1c) y x x (5 x 2) 2 15 15 5 dy 5 4 1 1 4 1 x x dx 15 5 3 5
  8. 8. x 2 2x 1e) y x2 1 x2 2x 1 ( x 1)( x 1) ( x 1) x2 1 ( x 1)( x 1) ( x 1) dy ( x 1)[1] ( x 1)[1] dx ( x 1) 2 x 1 x 1 ( x 1) 2 2 ( x 1) 2
  9. 9. Question: 6 (January 2010)
  10. 10. End ofPart 2

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