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Applications of Derivatives

Applications of Derivatives. Section 4.1 Section 5.2. Applications of Derivatives. Derivatives allow you to sketch the shape of functions. Applications of Derivatives. Ex: Amount of cargo unloaded at a port related to the number of trucks. Applications of Derivatives.

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Applications of Derivatives

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  1. Applications of Derivatives Section 4.1 Section 5.2

  2. Applications of Derivatives • Derivatives allow you to sketch the shape of functions

  3. Applications of Derivatives • Ex: Amount of cargo unloaded at a port related to the number of trucks

  4. Applications of Derivatives

  5. Applications of Derivatives

  6. Applications of Derivatives

  7. Applications of Derivatives

  8. Applications of Derivatives

  9. Applications of Derivatives

  10. Applications of Derivatives

  11. Applications of Derivatives • Sketch the function c(w) based on the following: c(0) = 200 c(5) = 176 c(20) = 121 c’(0) = -50 c’(5) = -44 c’(20) = -30

  12. Applications of Derivatives • Derivatives allow you to approximate functions

  13. Applications of Derivatives

  14. Applications of Derivatives

  15. Applications of Derivatives

  16. Applications of Derivatives

  17. Applications of Derivatives

  18. Applications of Derivatives

  19. Applications of Derivatives

  20. Applications of Derivatives • Suppose that for the function c(w), c(10) = 155 and c’(10) = -39. What is the approximate value of c(20)?

  21. Extreme Points 0 + slope - slope

  22. Extreme Points Population of Cleveland

  23. Extreme Points

  24. Extreme Points

  25. Extreme Points

  26. Extreme Points • Conclusions • At the minimum/maximum values of a function, the value of the derivative is 0. • At the inflection points of a function, the value of the derivative reaches a minimum/maximum.

  27. Extreme Points • Finding roots • Easy for linear, quadratic • Hard for higher order polynomials, other function Y= GRAPH CALC 2: zero

  28. Extreme Points • In-Class • Find the maxima and minima for the following functions • 0.04x3 - 0.88x2 + 4.81x +12.11 • 0.0004x4 – 0.007x3 + 0.03x2 – 0.035x + 10

  29. Extreme Points • Cost of production • How many machines are needed to minimize the cost per unit?

  30. Extreme Points

  31. Extreme Points

  32. Extreme Points • Fit a quadratic model to the data

  33. Extreme Points • How many machines are needed to minimize the cost per unit?

  34. Extreme Points

  35. Extreme Points • How many machines are needed to minimize the cost per unit? • The number that sets c’(m) = 0 (root)

  36. Extreme Points • Revenue over time • In what month was revenue maximized?

  37. Extreme Points

  38. Extreme Points

  39. Extreme Points • Fit a quartic model to the data

  40. Extreme Points • In what month was revenue maximized?

  41. Extreme Points

  42. Extreme Points • In what month was revenue maximized? • Find the 3 numbers that set r’(t) = 0 Y= GRAPH CALC 2: zero

  43. Extreme Points • In what month was revenue maximized? • Find the 3 numbers that set r’(t) = 0

  44. Extreme Points

  45. Extreme Points • In-Class

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