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**sherpa tensing****Member**- Registered: 2014-04-07
- Posts: 6

Good day to you all

The older I get the more I think of how I should have applied myself at school. My Father always used to say " I wish I could put an old head on young shoulders"......what? but I know what he meant now.! When I became a father myself I tried to help my daughters with their homework, I was ok with the basic stuff but had completely forgotten all about Algebra. I set about to rectfy this when I was 37, I enrolled at the local college for an evening class for GCE/GCSE in mathematics. Well, of course, now I had to apply myself, with 2 daughters on my case and 25 or so teenagers re-sitting the exam. I loved it, I went home after ever lesson, yes!, not to the pub, home, and did my homework like a proper swot. I enjoyed it so much I couldn't wait for the day of the lesson to come around.

I took the exam and got a "C" in the GCE exam and an "A" in the GCSE exam, so feeling quite proud of myself I sat back on my laurels. But now much later in life I've had an idea I might want to teach myself Calculus. Some of it sinks it (very slowly you understand!) but all of it facinates me, So, here I am, please be kind to me, when I put a query on the forum.

Regards Sherpa Tensing

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,380

hi Sherpa Tensing

**Welcome to the forum.**

Be kind. Of course; aren't we always?

Have you looked here yet:

http://www.mathsisfun.com/calculus/introduction.html

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,366

Hi sherpa tensing;

Welcome to the forum.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,531

Hello sherpa tensing.

We can help you by listing some excellent resources, but it depends on how you want to do it. Do you want to learn the more common but ridiculous high-school level math or the more rigorous form?

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**sherpa tensing****Member**- Registered: 2014-04-07
- Posts: 6

Gentlemen?

Thank you so much for your prompt replies.

Firstly in answer to you Bob, yes I have been on your suggested link and found it very informative with integration and differentiation. I write all the formulae down to make it "sink In" and slowly it does.

Secondly to answer you ShivamS last year I bought a Letts Edexcel guide to GCSE Maths question work book and by my standards I sailed through it, bar for things like "sets" and sequences. Suffering from delusions of granduer I have recently bought Letts guide to AS & A2 revision for maths. now, this where mathematics gets serious as you people know. I have had a certain amount of success, but the only problem is the book assumes prior knowlledge of higher level maths, which at the moment my knowledge is limited, but the spirit is very willing and I have the time neccessary. This level will be my limit I think.

Thirdly, Thank you bobbym keep in touch and we'll see how I progress. I have a particular problem with a quadratic equation (not with the formula) but one associated with completing the square. I shall post it tomorrow and If any of you can help me I will be able to sleep at nights. Talking of sleep I'm off now, I need my beauty sleep...........unlike you people.

Good night

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,531

Okay. I highly recommend that you take the more rigorous route (you learn a lot more and you understand a lot - for example, you said you wrote down the formulas, which is the wrong way. You need to understand why they work first). If you are still not convinced, then just go through a standard book like Stewart for Calculus.

By the way, you should have techniques like completing the square under your belt before learning calculus.

*Last edited by ShivamS (2014-04-07 09:07:59)*

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,366

I have a particular problem with a quadratic equation (not with the formula) but one associated with completing the square. I shall post it tomorrow and If any of you can help me I will be able to sleep at nights.

I never knew completing the square was a sedative. I checked the page and you are right it says,"do not drive or operate heavy machinery after completing the square!"

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 14,410

Hi sherpa tensing,

**Welcome to the forum!**

Character is who you are when no one is looking.

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**sherpa tensing****Member**- Registered: 2014-04-07
- Posts: 6

]Hello bobbym

Here is the problem that has kept me awake for a few nights

State the minimum value of 2x²-12x+11

This is how the book does it.....it says complete the square and simplify

2x²-12x+11 = 2(x²-6x) + 11 (I'm ok so far)

= 2((x-3)² -9) +11 (hmmm? why is -9 not plus 9 when the coefficient of "b" is -6 ie (b/2)²)

=2(x-3²) -7 ..............and where that -7 has come from God only knows......oh! and you bobbym of course?

I can see that when x = 3 that is when y has its minimum value, but how?

Can you help please then I can rest easily at night!

Hi ShivamS

I take your point onboard about learning the technique of "completing the square" which i will pursue vigorously. Also I bought a book called Calculus for Dummies (aptly, any good?) where there again it assumes plenty of prior knowledge of the subject, it could be a long job!

Hi to you also ganesh thank you for your welcome

Regards Sherpa T

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,366

Hi;

First:

Since they are trying to replace x^2 -6x they have to subtract 9 to do that.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,531

sherpa tensing wrote:

]Hello bobbym

Here is the problem that has kept me awake for a few nightsState the minimum value of 2x²-12x+11

This is how the book does it.....it says complete the square and simplify2x²-12x+11 = 2(x²-6x) + 11 (I'm ok so far)

= 2((x-3)² -9) +11 (hmmm? why is -9 not plus 9 when the coefficient of "b" is -6 ie (b/2)²)

=2(x-3²) -7 ..............and where that -7 has come from God only knows......oh! and you bobbym of course?

I can see that when x = 3 that is when y has its minimum value, but how?Can you help please then I can rest easily at night!

Hi ShivamS

I take your point onboard about learning the technique of "completing the square" which i will pursue vigorously. Also I bought a book called Calculus for Dummies (aptly, any good?) where there again it assumes plenty of prior knowledge of the subject, it could be a long job!Hi to you also ganesh thank you for your welcome

Regards Sherpa T

I think the question needs to be stated properly. I think what you are asking is:

Find the minimum y-value of y = 2x^2 -12x + 11

You can solve this in 4 ways. Factoring, completing the square, graphing the parabola or what is usually referred to as "partial factoring." The easiest method is completing the square though.

y = 2x^2 -12x + 11 = 2(x^2 - 6x) + 11 = 2(x^2 -2(3)x + 9 - 9) + 11

Note that x^2 -2(3)x + 9 is a perfect square and therefore can be written as (x-3)^2

y = 2((x-3)^2 - 9) + 11

Now, distribute the 2:

y = 2(x-3)^2 - 18 + 11 =2(x-3)^2 -7 Obviously, the minimum value is -7.

As for my opinion on "Calculus for Dummies," I think it is **the most ridiculous book in existence**. However, if you don't want a rigorous treatment of calculus, then that book is enough to give you a frivolous understanding of the subject - albeit a very bad one. I don't recommend it at all, but of course it's your choice.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,366

Hi;

Also I bought a book called Calculus for Dummies (aptly, any good?)

I prefer "Calculus Made Easy."

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**sherpa tensing****Member**- Registered: 2014-04-07
- Posts: 6

ShivamS wrote:

sherpa tensing wrote:]Hello bobbym

Here is the problem that has kept me awake for a few nightsState the minimum value of 2x²-12x+11

This is how the book does it.....it says complete the square and simplify2x²-12x+11 = 2(x²-6x) + 11 (I'm ok so far)

= 2((x-3)² -9) +11 (hmmm? why is -9 not plus 9 when the coefficient of "b" is -6 ie (b/2)²)

=2(x-3²) -7 ..............and where that -7 has come from God only knows......oh! and you bobbym of course?

I can see that when x = 3 that is when y has its minimum value, but how?Can you help please then I can rest easily at night!

Hi ShivamS

I take your point onboard about learning the technique of "completing the square" which i will pursue vigorously. Also I bought a book called Calculus for Dummies (aptly, any good?) where there again it assumes plenty of prior knowledge of the subject, it could be a long job!Hi to you also ganesh thank you for your welcome

Regards Sherpa T

I think the question needs to be stated properly. I think what you are asking is:

Find the minimum y-value of y = 2x^2 -12x + 11

You can solve this in 4 ways. Factoring, completing the square, graphing the parabola or what is usually referred to as "partial factoring." The easiest method is completing the square though.

y = 2x^2 -12x + 11 = 2(x^2 - 6x) + 11 = 2(x^2 -2(3)x + 9 - 9) + 11

Note that x^2 -2(3)x + 9 is a perfect square and therefore can be written as (x-3)^2

y = 2((x-3)^2 - 9) + 11

Now, distribute the 2:

y = 2(x-3)^2 - 18 + 11 =2(x-3)^2 -7 Obviously, the minimum value is -7.As for my opinion on "Calculus for Dummies," I think it is

the most ridiculous book in existence. However, if you don't want a rigorous treatment of calculus, then that book is enough to give you a frivolous understanding of the subject - albeit a very bad one. I don't recommend it at all, but of course it's your choice.

Hi ShivamS

I failed completely to, as you say "distribute the 2". When you lay it out, the -9 obviously becomes -18 +11 = -7 Bingo. I only paid £4 for Calculus for Dummies (second hand) so its not the end of the world. I will have a look around for Stewart for Calculus and give it a go. Practice looks like the order of the day for me and being methodical in my working out, meanwhile zzzzzzzzzzzzz

thank you

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**ShivamS****Member**- Registered: 2011-02-07
- Posts: 3,531

You're welcome. You can find Stewart for little money on abebooks.com

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