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Maxima and Minima of Functions. Maxima and minima of functions occur where there is a change from increasing to decreasing, or vice versa. Maxima and Minima of Functions. Maxima and minima of functions occur where there is a change from increasing to decreasing, or vice versa. 4. -3.

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Presentation Transcript
slide1

Maxima and Minima of Functions

Maxima and minima of functions occur where there is a change from increasing to decreasing, or vice versa.

slide2

Maxima and Minima of Functions

Maxima and minima of functions occur where there is a change from increasing to decreasing, or vice versa.

4

-3

slide3

Maxima and Minima of Functions

Maxima and minima of functions occur where there is a change from increasing to decreasing, or vice versa.

Relative Max.

4

-3

slide4

Maxima and Minima of Functions

Maxima and minima of functions occur where there is a change from increasing to decreasing, or vice versa.

Relative Max.

Relative Min.

4

-3

slide12

Maxima and Minima of Functions

DECREASING

INCREASING

slide22

Maxima and Minima of Functions

INCREASING

DECREASING

INCREASING

slide23

Maxima and Minima of Functions

Relative Maximum

Relative Minimum

slide25

Maxima and Minima of Functions

The difference in this example is we are restricted to a specific interval. So the edges of the interval will act as critical points along with the ones we find using the first derivative. They will be relative max or min depending on their position.

slide26

Maxima and Minima of Functions

The difference in this example is we are restricted to a specific interval. So the edges of the interval will act as critical points along with the ones we find using the first derivative. They will be relative max or min depending on their position.

Moving left to right :

If the edge has a decreasing arrow following, it is a relative maximum.

If the edge has an increasing arrow following, it is a relative minimum.

If the edge has a decreasing arrow in front of it, it is a relative minimum.

If the edge has an increasing arrow in front of it, it is a relative maximum.

slide27

Maxima and Minima of Functions

Moving left to right :

If the edge has a decreasing arrow following, it is a relative maximum.

If the edge has an increasing arrow following, it is a relative minimum.

If the edge has a decreasing arrow in front of it, it is a relative minimum.

If the edge has an increasing arrow in front of it, it is a relative maximum.

slide28

Maxima and Minima of Functions

Moving left to right :

If the edge has a decreasing arrow following, it is a relative maximum.

If the edge has an increasing arrow following, it is a relative minimum.

If the edge has a decreasing arrow in front of it, it is a relative minimum.

If the edge has an increasing arrow in front of it, it is a relative maximum.

slide29

Maxima and Minima of Functions

Moving left to right :

If the edge has a decreasing arrow following, it is a relative maximum.

If the edge has an increasing arrow following, it is a relative minimum.

If the edge has a decreasing arrow in front of it, it is a relative minimum.

If the edge has an increasing arrow in front of it, it is a relative maximum.

slide30

Maxima and Minima of Functions

Moving left to right :

If the edge has a decreasing arrow following, it is a relative maximum.

If the edge has an increasing arrow following, it is a relative minimum.

If the edge has a decreasing arrow in front of it, it is a relative minimum.

If the edge has an increasing arrow in front of it, it is a relative maximum.

slide31

Maxima and Minima of Functions

Moving left to right :

If the edge has a decreasing arrow following, it is a relative maximum.

If the edge has an increasing arrow following, it is a relative minimum.

If the edge has a decreasing arrow in front of it, it is a relative minimum.

If the edge has an increasing arrow in front of it, it is a relative maximum.

slide32

Maxima and Minima of Functions

Moving left to right :

If the edge has a decreasing arrow following, it is a relative maximum.

If the edge has an increasing arrow following, it is a relative minimum.

If the edge has a decreasing arrow in front of it, it is a relative minimum.

If the edge has an increasing arrow in front of it, it is a relative maximum.

slide33

Maxima and Minima of Functions

Moving left to right :

If the edge has a decreasing arrow following, it is a relative maximum.

If the edge has an increasing arrow following, it is a relative minimum.

If the edge has a decreasing arrow in front of it, it is a relative minimum.

If the edge has an increasing arrow in front of it, it is a relative maximum.

slide34

Maxima and Minima of Functions

Relative Maximum

Moving left to right :

If the edge has a decreasing arrow following, it is a relative maximum.

If the edge has an increasing arrow following, it is a relative minimum.

If the edge has a decreasing arrow in front of it, it is a relative minimum.

If the edge has an increasing arrow in front of it, it is a relative maximum.

slide35

Maxima and Minima of Functions

Relative Maximum

This is neither because there is no change in increasing/decreasing. It is called an “inflection point” which we will discuss later…

Moving left to right :

If the edge has a decreasing arrow following, it is a relative maximum.

If the edge has an increasing arrow following, it is a relative minimum.

If the edge has a decreasing arrow in front of it, it is a relative minimum.

If the edge has an increasing arrow in front of it, it is a relative maximum.

slide36

Maxima and Minima of Functions

Relative Maximum

Relative Minimum

Change from decreasing to increasing…

Moving left to right :

If the edge has a decreasing arrow following, it is a relative maximum.

If the edge has an increasing arrow following, it is a relative minimum.

If the edge has a decreasing arrow in front of it, it is a relative minimum.

If the edge has an increasing arrow in front of it, it is a relative maximum.

slide37

Maxima and Minima of Functions

Relative Maximum

Relative Maximum

Relative Minimum

Moving left to right :

If the edge has a decreasing arrow following, it is a relative maximum.

If the edge has an increasing arrow following, it is a relative minimum.

If the edge has a decreasing arrow in front of it, it is a relative minimum.

If the edge has an increasing arrow in front of it, it is a relative maximum.