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TRENDS & RELATIVE EXTREMES - PowerPoint PPT Presentation

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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PowerPoint Slideshow about 'TRENDS & RELATIVE EXTREMES' - PamelaLan

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• 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]

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

M20 L29: Trends and Relative Extremes -- Slide 2

• 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.

M20 L29: Trends and Relative Extremes -- Slide 4

M20 L29: Trends and Relative Extremes -- Slide 5

M20 L29: Trends and Relative Extremes -- Slide 6

M20 L29: Trends and Relative Extremes -- Slide 7

M20 L29: Trends and Relative Extremes -- Slide 8

M20 L29: Trends and Relative Extremes -- Slide 9