Trends relative extremes
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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

  • 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]


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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


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M20 L29: Trends and Relative Extremes -- Slide 2


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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.


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M20 L29: Trends and Relative Extremes -- Slide 4


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M20 L29: Trends and Relative Extremes -- Slide 5


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M20 L29: Trends and Relative Extremes -- Slide 6


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M20 L29: Trends and Relative Extremes -- Slide 7


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M20 L29: Trends and Relative Extremes -- Slide 8





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M20 L29: Trends and Relative Extremes -- Slide 9


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