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TRENDS & RELATIVE EXTREMESPowerPoint Presentation

TRENDS & RELATIVE EXTREMES

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TRENDS & RELATIVE EXTREMES

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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]

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

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