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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