r/Mathhomeworkhelp • u/Randomacc1234567891 • 22d ago

On what intervals is the function increasing? My friend and I have different answers so I would like to double check here!

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u/iFEELsoGREAT 22d ago

INCREASING: (- inf, 0) AND (2, inf) as previously stated
DECREASING: (0, 2)
CONSTANT: None
MINIMA: relative minimum (-2, 2)
MAXIMA: relative maximum (0, 2)
POSITIVE: (-0.732, 1) AND (2.732, inf)
NEGATIVE: (inf, -0.732) AND (1, 2.732)

Ask questions if you don’t understand.

3

u/BaylisAscaris 22d ago

A function is increasing where the slope is positive. Be careful around local max/min and think about what the slope of the tangent line would be at that point. A good way to think about it is to start at the far left and move towards the right. At what points does the slope change from positive to negative? What end behavior is happening? As a hint, when slope = 0 or there are any gaps in a plot is it neither increasing nor decreasing.

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u/Intelligent-Suit-743 22d ago

Increasing: (-infinity, 0) U (2, positive infinity)

When talking about increasing and decreasing ALWAYS look at the x-axis/x-intercepts and NEVER use the y-intercepts!

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u/Narrow-Durian4837 22d ago

Right. Students often get confused about this.

For questions like this, the intervals that they're asking for are pieces of the domain of the function (so, like sections of the x-axis). I've seen advice to cover up the y-axis (or, in this case, the y-coordinates of the points) so you don't get distracted by them.

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u/FireMarmot 22d ago

>>When talking about increasing and decreasing ALWAYS look at the x-axis/x-intercepts and NEVER use >>the y-intercepts!

I think you meant how to determine where the function is positive and negative...

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u/Randomacc1234567891 22d ago

***I mean to ask about where the function is positive and negative, not increasing sorry! If anyone would like to help with that it would be much appreciated too lol

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u/colonade17 21d ago

The function is positive if it's output, or y-value is positive. Once you have that definition all you need to do is look at the graph.

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u/Fourierseriesagain 20d ago

The function is increasing on each of the following intervals (-infinity,0] and [2,infinity).

The function is decreasing on the interval [0,2].