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TRENDS & RELATIVE EXTREMES

TRENDS & RELATIVE EXTREMES. SIGN OF THE FIRST DERIVATIVE LOCATING EXTREMES CUBIC EXAMPLE [I] Sign Graph and Factor Graph of f '(x) Sketch of f(x) QUINTIC EXAMPLE [4.5] REVENUE EXAMPLE [6] SEAGULL FUNCTION [7]. Since the derivative of f is negative for x<0 and positive for x>0,

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TRENDS & RELATIVE EXTREMES

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  1. TRENDS & RELATIVE EXTREMES • SIGN OF THE FIRST DERIVATIVE • LOCATING EXTREMES • CUBIC EXAMPLE [I] • Sign Graph and Factor Graph of f '(x) • Sketch of f(x) • QUINTIC EXAMPLE [4.5] • REVENUE EXAMPLE [6] • SEAGULL FUNCTION [7]

  2. Since the derivative of f is negative for x<0 and positive for x>0, we know f \ for x<0 and f / for x>0. This is borne out in the graph of f. M20 L29: Trends and Relative Extremes -- Slide 1

  3. M20 L29: Trends and Relative Extremes -- Slide 2

  4. LOCATING EXTREMES • If part of the graph of f has slope formula f ', then that part of the graph of f is continuous (connected) • If f ' is positive on a open interval, f is INcreasing there. • If f ' is negative on a open interval, f is DEcreasing there. • If an interval of increase connects with an interval of decrease, then f has a local maximum or minimum value there, depending on whether the increase is on the left or the right.

  5. M20 L29: Trends and Relative Extremes -- Slide 4

  6. M20 L29: Trends and Relative Extremes -- Slide 5

  7. M20 L29: Trends and Relative Extremes -- Slide 6

  8. M20 L29: Trends and Relative Extremes -- Slide 7

  9. M20 L29: Trends and Relative Extremes -- Slide 8

  10. A QUINTIC EXAMPLE [4,5]

  11. A REVENUE EXAMPLE [6]

  12. THE SEAGULL FUNCTION [7]

  13. M20 L29: Trends and Relative Extremes -- Slide 9

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