isiaiah d
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Hi,
The questions says:
by considering the behaviour of the function f(x) = x^3-8x-3 show that one root lies in the interval (-1,0) and another ies in the interval (-3,-1)

So far I found that there are maxima /minima at x= rt(8/3) and -rt(8/3) also the x-intercept is -3. not sure where to go from here?
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RDKGames
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(Original post by isiaiah d)
Hi,
The questions says:
by considering the behaviour of the function f(x) = x^3-8x-3 show that one root lies in the interval (-1,0) and another ies in the interval (-3,-1)

So far I found that there are maxima /minima at x= rt(8/3) and -rt(8/3) also the x-intercept is -3. not sure where to go from here?
You dont need to find maxima/minima.

The behaviour of that cubic is that it begins at -ve infinity, goes up to a local max, then goes down to a local min, and then shoots off to +ve infinity. So we can have up to three roots.

Since this is one continuous curve, you can reason that since f(-1) and f(0) have different signs, there there must be some value in the interval (-1,0) for which we have f=0. This is the same as showing that one of the roots lies in the interval (-1,0). Same approach for (-3,-1).
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isiaiah d
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(Original post by RDKGames)
You dont need to find maxima/minima.

The behaviour of that cubic is that it begins at -ve infinity, goes up to a local max, then goes down to a local min, and then shoots off to +ve infinity. So we can have up to three roots.

Since this is one continuous curve, you can reason that since f(-1) and f(0) have different signs, there there must be some value in the interval (-1,0) for which we have f=0. This is the same as showing that one of the roots lies in the interval (-1,0). Same approach for (-3,-1).
ahh, I thought it might be something like that, when a question says show ... though when am I allowed to use what they have included? I assumed I would have to show that a root was in the interval without using the interval they gave us?
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RDKGames
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(Original post by isiaiah d)
ahh, I thought it might be something like that, when a question says show ... though when am I allowed to use what they have included? I assumed I would have to show that a root was in the interval without using the interval they gave us?
Not sure what you mean. Of course you can use what they give you.
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isiaiah d
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(Original post by RDKGames)
Not sure what you mean. Of course you can use what they give you.
I thought the whole point of a proof/show that was that you were meant to get there without using it?
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the bear
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(Original post by isiaiah d)
So far I found that there are maxima /minima at x= rt(8/3) and -rt(8/3) also the x-intercept is -3. not sure where to go from here?
do you mean the y intercept is at ( 0, -3 ) ?
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isiaiah d
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(Original post by the bear)
do you mean the y intercept is at ( 0, -3 ) ?
Yup, im really rusty, pretty worrying since I start uni in a few weeks
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RDKGames
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(Original post by isiaiah d)
I thought the whole point of a proof/show that was that you were meant to get there without using it?
Yeah we didn't use the fact that there's a root in that interval to show there's a root in that interval. It's fine.
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