Psst.
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Find the values of x for which f(x) is an increasing function, given the f(x) equals:

 3 + 3x - 3x^2 + x^3
 f'(x) = 3 - 6x + 3x^2

Now I've sketched this graph and noticed it has a repeated root at 1 and that is probably why my answer isn't matching up with the answers.
So, Critical values:  (x-1)(3x-3) = 0
 x > 1
But this is wrong and the answers show  x \not=1 x \in \mathbb{R}

What does xER mean?
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Psst.
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TeeEm
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Zacken
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(Original post by Psst.)
Find the values of x for which f(x) is an increasing function, given the f(x) equals:

 3 + 3x - 3x^2 + x^3
 f'(x) = 3 - 6x + 3x^2

Now I've sketched this graph and noticed it has a repeated root at 1 and that is probably why my answer isn't matching up with the answers.
So, Critical values:  (x-1)(3x-3) = 0
 x > 1
But this is wrong and the answers show  x \not=1 x \in \mathbb{R}

What does xER mean?
A function f is strictly increasing if f' > 0.

In your case, you have f' = 3(x-1)^2 - it has a squared term that will always be positive, no matter what. Except... at x=-1 we have f' = 0 which means that the function is stationary there - it's not increasing.

So to summarise we have f' > 0 as long as x \neq -1. Whatever other value of x you wish to substitute into f' it will always be positive and hence the function will always be increasing.
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Psst.
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That made perfect sense.

Thank you Dr Zacken
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DylanJ42
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(Original post by Psst.)
x
You need to find the values of x where 3 - 6x + 3x^2 is >0. You worked out that it has a repeated root at x=1, so why don't you sketch 3x^2 - 6x + 3

As for x ∈ R (sorry I cannot latex this), I think it literally translates to x is contained in the Real Numbers

So basically x lies on the number line somewhere, so it includes all the integers, fractions, rational numbers, irrational numbers etc
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Simple_student
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(Original post by Psst.)
Find the values of x for which f(x) is an increasing function, given the f(x) equals:

 3 + 3x - 3x^2 + x^3
 f'(x) = 3 - 6x + 3x^2

Now I've sketched this graph and noticed it has a repeated root at 1 and that is probably why my answer isn't matching up with the answers.
So, Critical values:  (x-1)(3x-3) = 0
 x > 1
But this is wrong and the answers show  x \not=1 x \in \mathbb{R}

What does xER mean?
Hi I've seen this phrase on My C3 course :

XER means x can be any real numbers (pi, e, decimals fractions, mixed numbers, integers, etc..)


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Zacken
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(Original post by DylanJ42)
As for x ∈ R (sorry I cannot latex this), I think it literally translates to x is contained in the Real Numbers
\displaystyle x \in \mathbb{R}
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Zacken
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(Original post by Psst.)
 f'(x) = 3 - 6x + 3x^2

Now I've sketched this graph and noticed it has a repeated root at 1 and that is probably why my answer isn't matching up with the answers.
(Original post by DylanJ42)
so why don't you sketch 3x^2 - 6x + 3


@OP - you're welcome!
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DylanJ42
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(Original post by Zacken)
\displaystyle x \in \mathbb{R}
Noted, thank you
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DylanJ42
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(Original post by Zacken)


@OP - you're welcome!
:rofl: didn't read the post properly :facepalm:
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Zacken
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(Original post by DylanJ42)
:rofl: didn't read the post properly :facepalm:
I once wrote a 5 paragraph post only to realise that I missed a condition in the question that rendered all my working obsolete. So I deleted it.

Spoiler:
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An hour later, somebody posts something similar to what I was going to post - turns out it was a valid method, even with that condition. :facepalm:
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TeeEm
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(Original post by Psst.)
TeeEm
glad to see you got help as I am teaching until 23.15
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DylanJ42
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(Original post by Zacken)
I once wrote a 5 paragraph post only to realise that I missed a condition in the question that rendered all my working obsolete. So I deleted it.
Spoiler:
Show
An hour later, somebody posts something similar to what I was going to post - turns out it was a valid method, even with that condition. :facepalm:
Oh my god how horrible, at that stage I probably would have just posted it anyway and typed at the bottom "whoops didn't see the condition" :eek: on the bright side though, you wont be forgetting the method to answering whatever the particular question was any time soon

I'd say 5% of all my answers are slightly off just because I read what I want to read :laugh:
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