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Chapter 22: Applications of differential Calculus.

Chapter 22: Applications of differential Calculus. A. Serra. A. Properties of curves. In groups: discuss opening problem (page 648). Write notes in individual notebooks. Class work:

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Chapter 22: Applications of differential Calculus.

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  1. Chapter 22:Applications of differential Calculus. A. Serra

  2. A. Properties of curves In groups: discuss opening problem (page 648). Write notes in individual notebooks. Class work: Discuss increasing and decreasing intervals. Stationary points (f’(x)=0), Turning points (maxima and minima) and points of inflection. Sign diagrams. Exercise 22A1: 1,2 d Individual work: • Examples 1,2,3,4: Do them & check your answers. • Exercise 22A1: 1,2 (a,b,conly) • Exercise 22A2: 1,3(a,b,c only), 7 (a only). • Extra: 22A: Other exercises.

  3. B. Rates of change. CLASS WORK Remember: The instantaneous rate of change of a variable at a particular instant is given by the gradient of the tangent to the graph at that point…=f’(x)=dy/dx. Positive up, negative down. Example Exercise 22B1: 4 (page 657). INDIVIDUAL WORK • Examples 5 and 6: Do them & check your answers. • Exercise 22B.1: 3,5 • Exercises 22B.2: 3,5 • Extra: Other exercises in 22B

  4. C. Optimisation. CLASS WORK Testing optimal solutions. Sign diagram test & derivatives vs Graphing calculator. Group work: Investigation: The derivative of y=x^2 (page 635) INDIVIDUAL WORK • Examples 7 and 8: Do them & check your answers. • Exercise 22C: 1, 5, 7, 13. • Extra: Other exercises in 22C

  5. Review • INDIVIDUAL WORK • Review Set 22A. • Extra: Review Set 22B and/or 22C • NEXT • Chapter 23… and tests. • Good luck 

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