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shudnt_have
07-19-2006, 02:21 AM
If I am asked to find the constants a, b, c, d such that the graph of
f(x)= ax^3 + bx^2 + cx+ d has horizontal tangent lines at the points (-2, 1) and (0, -3).

I know though, the first thing I would do is, find the derivative of the function..."f(x)= ax^3 + bx^2 + cx+ d "

which would be...

f' (x) = 3 ax^2+ 2 bx+ c
then sub the value of x? x = (-2) into the last equation..
which will equal to
12 a- 4b+ c

I got no clue onwards..:D


and I have another q.


Given h= f 0 g, g(3)=7, g'(3)=4, f(2)=4, f'(7)=-6.
now how do I determine the h' (3)???

again i am half way through the answer...

I think thinking of solving it with product rule??
h(x)= f(g) x)) h(x)= f' (g(x) g'(x)

h' (x)= f' (g (3)= g'3= f' (7) (4) = (-6) (-4) = -24
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Skillganon
07-20-2006, 02:13 PM
Sis I don't have a clue!! . It's been a long time since my A-level math's. Perhaps you can give me a site to brush up my math's on that level.
Reply

Ameeratul Layl
07-20-2006, 02:16 PM
Salam,

I haven't done this yet, but if you provide the link (like br skillganon mentioned), then, I will have a go. It'll be fun!

Wasalam
Reply

Ameeratul Layl
07-20-2006, 04:43 PM
Salam sister (Shudnt_have),

I have found something that MAY help.

http://www.univie.ac.at/future.media...werkzeuge.html

I am studying deravatives to see if I can help. It sounds challenging!

Wasalam
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MH-UK
07-20-2006, 06:57 PM
Again been a long time since I did this kind of thing...

I got

a: 1
b: 3
c: 0
d: -3

Disclaimer: I might be wrong :p ... I'll have another look
Reply

MH-UK
07-20-2006, 07:25 PM
:sl:

Remember the gradient of a tangent line is the same as the gradient of the curve at the same point. Now, since both the tangents are horizontal lines (from the question), the gradients of both lines are then taken to have the value 1. This means then that the gradients of the curve at points (-2,1) and (0,-3) are also both 1:

Gradient of curve at [-2,1]: 12a - 4b + c = 1
Gradient of curve at [0,-3]: c = 1
I don't think the gradient of a horizontal line is 1. A gradient of 1 is like the y=x graph. I think gradient of a horizontal line is 0.

If you recalculate with this change you should get same anwser as me.

Now for the second question, no idea, I don't even understand the notation.

what is f 0 g ??
Reply

MH-UK
07-20-2006, 07:30 PM
Just had a thought, those two coordinates given are stationary points on the curve and at stationary points dy/dx is always zero because the sign of the curve has to change. eg from minus to plus or plus to minus, therefore passing through zero.

Eg. fig -
Reply

Ameeratul Layl
07-20-2006, 07:58 PM
Salam,

Br Alpha Dude and MH-UK could you kindly recommend a website that includes this topic and other AS topics. Please? This sounds really fun (challenging). I tried to understand the exercises on the links that I found, but they weren't very good.

Wasalam
Reply

lolwatever
07-30-2006, 10:53 AM
salams

bro alpha has the correct values of b,c and d, but a=+1

here's my working

f(x) = ax^3 + bx^2 + cx + d
f'(x) = 3ax^2 + 2bx + c
f'(-2) = 0 and f'(0) = 0

eq1. f'(-2) = 0 = 12a - 4b + c
eq2. f'(0) = 0 = c
eq3. f(-2) = 1 = -8a + 4b + d
eq4. f(0) = -3 = d

thrfore, c=0, d=-3 from eq2 and eq4 respectively.

sooo.. we can deal with these equations now (i subbed in c=0 and d=-3 into eq1 and eq3.

eq1. f'(-2) = 0 = 12a - 4b
eq3. f(-2) = 1 = -8a + 4b - 3

i simplified those two equatons to get

eq1. f'(-2) = 0 = 3a - b
eq3. f(-2) = 0 = -2a + b - 1

now, we have simple case of simultaneous equations. from eq1. we get
eq1 a = b/3

we can sub a=b/3 into eq3 and get

eq3 0 = -2b/3 + b -1

from that we get,

b = 3

therefore

now we can substitute b=3 into eq1 and get value for a

eq1 3a-3 = 0
a= 1

hence a=1, b=3, c=0, d=-3

now ill take a look at the 2nd problem n get bak2u later insahlah.. salams

ps: i'm not a math genuis, i suck at it.. i learnt calculus from rajuman's thread about 3=2.
Reply

lolwatever
07-30-2006, 11:07 AM
salams sis

as for the second problem.. we solve it using the chain rule

basically this is how the chain rule goes.

for the function h = f(g(x))

h'(x) = f'(g(x)) * g'(x)

sooo... therefore we can say

h'(3) = f'(g(3)) * g'(3) = f'(7) * 4 = -6 * 4 = -24

so yep ur right.. but that's called chain rule not product rule.
salams
Reply

lolwatever
07-30-2006, 11:33 AM
no prob :D














lol messing.. i proved you right too, you where correct in 3 of the 4 cases for a,b c, d :)
Reply

shudnt_have
08-16-2006, 12:42 AM
i dont thik i thanked everyone.
thankyou!:D for the help y'all
Reply

Jayda
08-20-2006, 05:35 PM
Hola Math Geniuses!

Now I need your help... this is very difficult. If I have 10,000 add 1% onto that then put the 1% back into the 10,000 and then repeat the process with 10,100 and continue like that for about 51 more times what would my end result be?
Reply

lolwatever
11-16-2006, 08:28 AM
heya jayda... could you explain it perhaps by presenting an example

i didnt quite understand the pattern.. but i got a feeling its to do with sequences and series..

take carea ll the best!
Reply

Curaezipirid
11-16-2006, 06:12 PM
Originally Posted by Jayda
Hola Math Geniuses!

Now I need your help... this is very difficult. If I have 10,000 add 1% onto that then put the 1% back into the 10,000 and then repeat the process with 10,100 and continue like that for about 51 more times what would my end result be?
are you adding 1% onto 10 000 to get 10 100
then also putting 1% back into the 10 000 which also sort of is 10 100
but how can we perform that operation twice
except that it is implicit in repeating the process with 10 100 that adding and putting back are the same
so 52 operations of add/put back 1% of 10 000

= a pattern that is definitely beyond the number at which I would assume that it continues in the same fashion as the earliest pattern which shows

eg. I might have said, if the question was only 41 more operations that the answer is like 14242

BUT after 42 the pattern most likely goes askew. But my self ain't going to sit down with pen and paper to make those calculations right now to know for certain. Fourty two has a stop probability higher than other numbers, and that ain't no superstition but a verifiable fact of logic.

Look at the safe curve by: 9>13>18>26>36>42.

However as far as derivatives and differentials go you lot are all far surpassing me. I learned late as a teenager by accident of a change of teacher and then over relied upon my father who is as often as not less accurate than I am (shhh). Then I had to relearn at University in which I remember distinctly looking at the measuring of a tangent with utter horror: "they can't do that!" So we stop at the fourty two, because the thirty six was bad enough, and the top of the range is the twenty six in this sum. (I hope the Mahdi sorts it all out.)

True it is often difficult for believers to comprehend calculus becasue in the real world what many of the set examples which are used are able to be deciphered into is that need for Jahannam to exist! There is only one example of calculus which is representative of Qur'an, and it is which ever example it is which causes the mind to orient to Revelations Isa made to St John the Evangelist.

But that is the utter limit of mathematical genius, and what is the meaning of the word genius anyhow? Is it derived from "genesis"? or at least having the same greek or latin root?
Reply

Curaezipirid
11-16-2006, 06:16 PM
Originally Posted by MH-UK
:sl:



I don't think the gradient of a horizontal line is 1. A gradient of 1 is like the y=x graph. I think gradient of a horizontal line is 0.

If you recalculate with this change you should get same anwser as me.

Now for the second question, no idea, I don't even understand the notation.

what is f 0 g ??
When is the horizon a horizontal line?;D
Reply

Curaezipirid
11-16-2006, 06:17 PM
And don't say barefoot in the f 0 g because it is barefoot among frogs
Reply

Curaezipirid
11-16-2006, 06:26 PM
But I don't get why there was a series of coincidences in respect of these posts aligned with the numbers:
111
84
5

Which are an interesting sequence.
Reply

lolwatever
11-16-2006, 06:50 PM
^ lol sis i think he's referring to f(g) when he says fog.... basically suppose you have a function

g(x) = x^2

and another function f,

f(x) = 3x+2

f(g) (fog) basically means you take g(x) and substitute x for g(x) in f(x)... so f(g) becomes:

f(g) = 3(x^2) + 2

I don't think the gradient of a horizontal line is 1. A gradient of 1 is like the y=x graph. I think gradient of a horizontal line is 0.
ya ur right... another way to look at it is.. if you take the hoirzontal line

y = 3

and take the derivative of that .... it would be zero. (derivative of a constant is zero).

or.. analysing it fromt he defintion of gradietn = 'rise/run'.... the rise of a horizontal line is zero.. so zero divided by one is zero

take care all the best
Reply

MH-UK
11-20-2006, 03:47 PM
:sl:

lolwatever, you're right, and from that argument you can say that a vertical line has a "run" of 0 and therefore you would be dividing by 0, which gives an infinite gradient I imagine....
Reply

lolwatever
11-21-2006, 02:03 AM
^ actually correct me if i'm wrong, but isn't the gradient of a veritcal line indeterminate? coz its like a cusp ? they only say its 'infinite' but you don't really get the value 'infinity' when you try find the gradient.

salams
Reply

zanjabeela
11-21-2006, 07:01 AM
:sl:
hahaha geek alert. I am out of here!
Reply

lolwatever
11-21-2006, 07:03 AM
Originally Posted by zanjabeela
:sl:
hahaha geek alert. I am out of here!
:lol: zAkjabeela can replace u :D
Reply

Younus
11-21-2006, 07:03 AM
Maths.... :eek: :grumbling
Reply

zanjabeela
11-21-2006, 07:20 AM
Originally Posted by lolwatever
:lol: zAkjabeela can replace u :D
There is no zAkjabeela on these premises. Treat the Super(b) Mod zAk with the respect he deserves. And more importantly don't pervert my name!

Back to the geekiness...
Reply

MH-UK
11-21-2006, 06:42 PM
:sl:

Perhaps you are right lolwatever....

I was thinking about dividing by a number which tends to 0....

like 0.000001, because when you do this you get a large number.

But I think I've confused myself lol

wa Allahu alam
Reply

Curaezipirid
11-22-2006, 11:48 AM
Originally Posted by lolwatever
^ lol sis i think he's referring to f(g) when he says fog.... basically suppose you have a function

g(x) = x^2

and another function f,

f(x) = 3x+2

f(g) (fog) basically means you take g(x) and substitute x for g(x) in f(x)... so f(g) becomes:

f(g) = 3(x^2) + 2



ya ur right... another way to look at it is.. if you take the hoirzontal line

y = 3

and take the derivative of that .... it would be zero. (derivative of a constant is zero).

or.. analysing it fromt he defintion of gradietn = 'rise/run'.... the rise of a horizontal line is zero.. so zero divided by one is zero

take care all the best
Are you trying to tell me that the function of a line with a gradient of zero has nothing to do with a frog, or what?...








.. . I thought about it and decided that this is only because frogs hop on a plane rather than a line, Salam=Waram mathematicians
Reply

lolwatever
11-22-2006, 11:58 AM
:lol: u seem to hav introduced another science, frogamatics :D
salamz
Reply

Curaezipirid
11-23-2006, 04:28 AM
Tiddalik is a really big frog who drinks up all the water, then all the animals have to try to make him laugh so that he coughs it all up.

It is an Aboriginal Dreamtime story which most Aussie children learn as a school play in infants school, and my house is right on the Dream line/Ley line, which that story belongs too. So truly I best not claim it to be my own science, though the idea fancies me.

Great minds think alike! (even when the tools in use take a different shape)
Reply

zanjabeela
11-23-2006, 04:58 AM
Originally Posted by Curaezipirid
Are you trying to tell me that the function of a line with a gradient of zero has nothing to do with a frog, or what?...


.. . I thought about it and decided that this is only because frogs hop on a plane rather than a line, Salam=Waram mathematicians
lol sister Curaezipirid...you and me are thinking the same thing...mathematicians! :muddlehea

:w:

;D ;D ;D
Reply

lolwatever
11-23-2006, 06:48 AM
Originally Posted by Curaezipirid
Tiddalik is a really big frog who drinks up all the water, then all the animals have to try to make him laugh so that he coughs it all up.

It is an Aboriginal Dreamtime story which most Aussie children learn as a school play in infants school, and my house is right on the Dream line/Ley line, which that story belongs too. So truly I best not claim it to be my own science, though the idea fancies me.

Great minds think alike! (even when the tools in use take a different shape)
so do dumb ones ;D


(i'm the dumb mind in this case nt u :hiding:)
Reply

Curaezipirid
11-30-2006, 05:34 AM
Mathematicians need constant suctioning from the rather plentiful examples of calculus they note down in pen and paper. Ever one that can exist is done. So best to never cognise another one. Each of the shaytan whom, in truth, are who will get that they did it, the moon, are in causation one set of tangential equivalences. Which is why I look no further, that that which proves that marxism can, since if I have to be an ist, rather marx than is lamb
Reply

lolwatever
12-25-2006, 11:46 AM
^lol :rollseyes, ok bak to topic.....
Reply

Jayda
12-27-2006, 02:29 PM
Originally Posted by lolwatever
heya jayda... could you explain it perhaps by presenting an example

i didnt quite understand the pattern.. but i got a feeling its to do with sequences and series..

take carea ll the best!
hola lolwatever,

for example, i am given $10,000 and decide to put it in a bank where i get 1% interest every week. each week i recieve 1% interest on my account, and i put that 1% interest i have collected right back into the account...

week 1: 10,000 + 1% = week 2: 10,100 + 1% = week 3: 10,201 +1% = week 4:

so on so forth for the duration of one year (52 weeks)... i am trying to find out what the total amount of money in the bank will be at the end of one year. and if somebody could explain the formula (i think it involves permutations?) i would be very grateful!

mucho gracias
annette
Reply

Jayda
12-27-2006, 02:34 PM
Originally Posted by Curaezipirid
are you adding 1% onto 10 000 to get 10 100
then also putting 1% back into the 10 000 which also sort of is 10 100
but how can we perform that operation twice
except that it is implicit in repeating the process with 10 100 that adding and putting back are the same
so 52 operations of add/put back 1% of 10 000

= a pattern that is definitely beyond the number at which I would assume that it continues in the same fashion as the earliest pattern which shows

eg. I might have said, if the question was only 41 more operations that the answer is like 14242

BUT after 42 the pattern most likely goes askew. But my self ain't going to sit down with pen and paper to make those calculations right now to know for certain. Fourty two has a stop probability higher than other numbers, and that ain't no superstition but a verifiable fact of logic.

Look at the safe curve by: 9>13>18>26>36>42.

However as far as derivatives and differentials go you lot are all far surpassing me. I learned late as a teenager by accident of a change of teacher and then over relied upon my father who is as often as not less accurate than I am (shhh). Then I had to relearn at University in which I remember distinctly looking at the measuring of a tangent with utter horror: "they can't do that!" So we stop at the fourty two, because the thirty six was bad enough, and the top of the range is the twenty six in this sum. (I hope the Mahdi sorts it all out.)

True it is often difficult for believers to comprehend calculus becasue in the real world what many of the set examples which are used are able to be deciphered into is that need for Jahannam to exist! There is only one example of calculus which is representative of Qur'an, and it is which ever example it is which causes the mind to orient to Revelations Isa made to St John the Evangelist.

But that is the utter limit of mathematical genius, and what is the meaning of the word genius anyhow? Is it derived from "genesis"? or at least having the same greek or latin root?

gracias Curaezipirid

this is close to i think what i am asking... are you reinvesting the 1% and taking account for that when you recalculate interest for the next week in the formula you worked out?

if i may ask could you perhaps clarify what you mean about Calculus representing the quran? that was very confusing to me... i do not understand those arabic words you used...

gracias
Reply

lolwatever
12-27-2006, 07:07 PM
Originally Posted by Jayda
hola lolwatever,

for example, i am given $10,000 and decide to put it in a bank where i get 1% interest every week. each week i recieve 1% interest on my account, and i put that 1% interest i have collected right back into the account...

week 1: 10,000 + 1% = week 2: 10,100 + 1% = week 3: 10,201 +1% = week 4:

so on so forth for the duration of one year (52 weeks)... i am trying to find out what the total amount of money in the bank will be at the end of one year. and if somebody could explain the formula (i think it involves permutations?) i would be very grateful!

mucho gracias
annette
Heya Jayda,

Ok here's the formula we gonna use:

I = C(1+ (r/100))^n

It's called the 'compound interest' equation, compound basically means... the interest given to your account keeps getting fed back in and the interest is 're-applied' to it.. so on and so forth.

I'll define the terms:

I = Final value of investment.
C = Initial Capital invested (10,000)
r = Interest Paid to your investment. (1%)
n = time period (in our case, 52 weeks)

Plugging in the values:

I = C * (1+ (r/100))^n

I = 10,000 * ( 1+ (1/100) ) ^ 52

simplifying...

I = 10,000 * (1.01) ^ 52

plugging into calc.. we get..

I = 16,776.88921

converting it to a reasonable answer...

I = $16,776.90

Hope that helps :)


Take care all the best!
Reply

Jayda
12-27-2006, 07:30 PM
gracias!! you just helped me set up my first charity!

Dios te bendiga
Reply

lolwatever
12-28-2006, 01:28 AM
Originally Posted by Jayda
gracias!! you just helped me set up my first charity!

Dios te bendiga
lol no probs netime.


Originally Posted by Jayda
gracias Curaezipirid

this is close to i think what i am asking... are you reinvesting the 1% and taking account for that when you recalculate interest for the next week in the formula you worked out?

if i may ask could you perhaps clarify what you mean about Calculus representing the quran? that was very confusing to me... i do not understand those arabic words you used...

gracias
^ i think Cura was just mucking around. lol.. :rollseyes
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