Intervals of Increase and Decrease

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Presentation transcript:

Intervals of Increase and Decrease

Trace the function left to right.

The green intervals are going "up" and the blue interval is going "down".

3 The green intervals are going "up" and the blue interval is going "down". B A C D Is "up" and "down" vertical or  horizontal concepts? A. Vertical B. Horizontal

The green intervals are going "up" and the blue interval is going "down". Is "up" and "down" vertical or  horizontal concepts? A. Vertical B. Horizontal

Vertical concepts ( ) are named on horizontal intervals( ).

Let's put in coordinates for the local max. (15,20)

Let's put in coordinates for the local min. (15,20) (22,4)

Let's put in coordinates for the inflection point. (15,20) (32,20) (22,4)

Let's put in coordinates for the endings. (∞,∞) (15,20) (32,20) (22,4) (-∞,-∞)

Let's x out what we don't need.

On what interval(s) does this function increase? Interval of Increase

On what interval(s) does this function increase? Interval of Increase (-∞,15)∪(22,∞)

On what interval(s) does this function decrease? Interval of Decrease

On what interval(s) does this function decrease? Interval of Decrease (15,22)

Let's do another function (8, 50) (24, 50) (16, 32) (-6, 20)

If you were to give this ending coordinates, what would they be?

If you were to give this ending coordinates, what would they be? (-∞,∞)

If you were to give this ending coordinates, what would they be?

If you were to give this ending coordinates, what would they be? (∞,-∞)

Trace the function to find the intervals of increase and decrease. Interval of Decrease Interval of Increase

Trace the function to find the intervals of increase and decrease. Interval of Decrease Interval of Increase

Trace the function to find the intervals of increase and decrease. Interval of Decrease Interval of Increase

Trace the function to find the intervals of increase and decrease. Interval of Decrease Interval of Increase

Trace the function to find the intervals of increase and decrease. Interval of Decrease Interval of Increase

Trace the function to find the intervals of increase and decrease. Interval of Decrease Interval of Increase

Trace the function to find the intervals of increase and decrease. Interval of Decrease Interval of Increase

Trace the function to find the intervals of increase and decrease. Interval of Decrease Interval of Increase

Trace the function to find the intervals of increase and decrease. Interval of Decrease Interval of Increase

Trace the function to find the intervals of increase and decrease. Interval of Decrease Interval of Increase

Trace the function to find the intervals of increase and decrease. Interval of Decrease Interval of Increase

Trace the function to find the intervals of increase and decrease. Interval of Decrease Interval of Increase

Trace the function to find the intervals of increase and decrease. Interval of Decrease Interval of Increase

Trace the function to find the intervals of increase and decrease. Interval of Decrease Interval of Increase

Let's x out what we don't need. Interval of Decrease Interval of Increase

What is the interval of decrease? Interval of Increase

What is the interval of increase? Interval of Decrease Interval of Increase (-∞,-6)∪(8,16)∪(24,∞)

Let's determine the increasing and decreasing intervals for this function. (-18,16) (17,7) (12,5) (-10,5) (20,5) (14,-1)

What type of interval is this?

What type of interval is this? Constant Interval

Trace the function. (-18,16) (17,7) (12,5) (-10,5) (20,5) (14,-1)

Put in coordinates of the ending. (-18,16) (∞,-∞) (17,7) (12,5) (-10,5) (20,5) (14,-1) (-∞,-∞)

out what is not needed. (∞,-∞) (-∞,-∞) (-18,16) (17,7) (12,5) (-10,5) (20,5) (14,-1) (-∞,-∞)

Interval of Decrease Interval of Increase

Interval of Decrease Interval of Increase (-18,-10)∪(12,14)∪(17,20) (-∞,-18)∪(14,17)∪(20,∞)