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TRENDS & RELATIVE EXTREMES

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Lesson 29 4.1 - PowerPoint PPT Presentation


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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
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]
slide2

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

locating extremes
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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