# Increasing & Decreasing Functions

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Thread starter 4 years ago
#1
Find the values of x for which f(x) is an increasing function, given the f(x) equals:

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:

But this is wrong and the answers show

What does xER mean?
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Thread starter 4 years ago
#2
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4 years ago
#3
(Original post by Psst.)
Find the values of x for which f(x) is an increasing function, given the f(x) equals:

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:

But this is wrong and the answers show

What does xER mean?
A function is strictly increasing if .

In your case, you have - it has a squared term that will always be positive, no matter what. Except... at we have which means that the function is stationary there - it's not increasing.

So to summarise we have as long as . Whatever other value of you wish to substitute into it will always be positive and hence the function will always be increasing.
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Thread starter 4 years ago
#4
That made perfect sense.

Thank you Dr Zacken
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4 years ago
#5
(Original post by Psst.)
x
You need to find the values of x where is >0. You worked out that it has a repeated root at x=1, so why don't you sketch

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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4 years ago
#6
(Original post by Psst.)
Find the values of x for which f(x) is an increasing function, given the f(x) equals:

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:

But this is wrong and the answers show

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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4 years ago
#7
(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
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4 years ago
#8
(Original post by Psst.)

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

@OP - you're welcome!
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4 years ago
#9
(Original post by Zacken)
Noted, thank you
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4 years ago
#10
(Original post by Zacken)

@OP - you're welcome!
didn't read the post properly
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4 years ago
#11
(Original post by DylanJ42)
didn't read the post properly
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.
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4 years ago
#12
(Original post by Psst.)
TeeEm
glad to see you got help as I am teaching until 23.15
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4 years ago
#13
(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.
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" 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
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