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All u calculus majors i need halp!!!!!

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laxstar
Posts: 1051 - Karma: 11
we have a little homework problem thing for my calculus class and i don't really know what im doing i hope someone can help me out.

Given the function F(x)= 4x^2 - 2x + 6, find the derivative function F'(x) using the definition of the derivative.

not the hardest problem i just don't understand the definition of the derivative, so if any one could help me or do it for that would be cool..
Feb 8 2009 8:44PM
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Commonwealth
Posts: 3729 - Karma: 11
wouldn't that just be the derivative?

F'(x) = 8x - 2

I forgot the original function already though. So those numbers might not be right.
Feb 8 2009 8:49PM
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bsmith01
Posts: 1639 - Karma: 43
Well I know the answer is 8x-2 but I dont remember how to use the definition of the derivative.  I think it had something to do with taking limits.  I guess I wasnt much help, sorry.
Feb 8 2009 8:50PM
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laxstar
Posts: 1051 - Karma: 11
sorrry i wasnt clear i know how to find the answer i just need the work of the actual derivitive function...
its like

F'(x)= F(x-h) - F(x) divided by h
      
Feb 8 2009 8:51PM
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jmath
Posts: 112 - Karma: 11
I'm pretty sure that the definition of a derivative the limit? so wouldn't it be [f(x+h)-f(x)]/h then take the limit of that as h approaches infinite
Feb 8 2009 8:52PM
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put
Posts: 36 - Karma: 10
definition of derivitive means  f '(x) = f(x + delta x) - f(x)  all over delta x
Feb 8 2009 8:52PM
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laxstar
Posts: 1051 - Karma: 11
does anyone feel like plugging this stuff in for me?? and get it going karma will be given
Feb 8 2009 8:54PM
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^nate^
Posts: 1263 - Karma: 560

Given the function F(x)= 4x^2 - 2x + 6, find the derivative function F'(x) using the definition of the derivative.

So the definition of a derivative is

f ' (x) = Limit as h goes to 0: (f(x+h)-f(x))/h

so: (4(x + h)^2 - 2(x + h) + 6) - (4x^x - 2x + 6))/h

you're going to want to expand that out and then cancel out as many "h's" as you can with the quotient. And then whatever "h's" you have left go to zero, because the derivative is defined as when h->0. So the last h's will just go to zero and you'll be left with you answer, which should be 8x - 2

Feb 8 2009 8:56PM
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Pisces
Posts: 905 - Karma: 13

F(x)= 4x^2 - 2x + 6

lim      {4(x+h)^2-2(x+h)+6-(4x^2-2x+6)}/

h-->0                      h

something like that i think? honestly i dont remember anymore, done with calculus but i vaguely remember it being the limit as h approaches 0 of f(x+h)-f(x)/h

Feb 8 2009 8:59PM
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laxstar
Posts: 1051 - Karma: 11
ty to everyone your karma was adjusted....
Feb 8 2009 9:45PM
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chapz
Posts: 10182 - Karma: 66
isnt it like the limit of f(x) - f(a) over x minus a as xgoes to infinity?

or F(x)= 4x^2 - 2x + 6 --> F'(x)=8x - 2
Feb 8 2009 10:18PM
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Pisces
Posts: 905 - Karma: 13
honestly the definition of a derivitive won't help much at all. it is just used to help understand the process of finding a derivtive from one point of view before any shortcuts are shown. however, and unfortunately i add in my opinion, derivitives and integrals are an extremely important part of a lot of jobs. as i take business classes im actually starting to understand the point of them after taking calculus where i thought they were usueless.
Feb 8 2009 10:29PM
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Mr_W00
Posts: 164 - Karma: 12
i hate calculus it rapes my mind
Feb 8 2009 10:32PM
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comeatmebro
Posts: 10720 - Karma: 66
shit i am in calc and have never learned any of this.
Feb 8 2009 10:37PM
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comeatmebro
Posts: 10720 - Karma: 66
please, just ignore this comment.
Feb 8 2009 10:38PM
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Slinger1x1
Posts: 8853 - Karma: 66
wait, this is calc for college? im a sophomore in HS and i know this stuff...

but im mad good at math, im in like juniors advanced math as a sophomore. just comes natural, i dont study and i have a solid 3.5
Feb 8 2009 10:40PM
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chapz
Posts: 10182 - Karma: 66
this is just basic cal 1 i believe. or at least i learned this in cal 1
Feb 8 2009 10:46PM
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^nate^
Posts: 1263 - Karma: 560
congrats man! that's so aweosme! u must be so good. thanks for telling everyone.
Feb 8 2009 10:49PM
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ClownPrince
Posts: 500 - Karma: 10
I think there's some difference. Calc classes in college (at least at my school) move a lot faster and cover a lot less than high school classes, because what takes a semester in college (calc 1 in this case) usually takes a year in high school.

But I agree, I took this stuff in high school too and thought it was easy. Never studied either...you'll learn when you get to college (depending on where you go).
Feb 8 2009 10:51PM
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laxstar
Posts: 1051 - Karma: 11
yea calc basically mind fucks me, but this shit is easy i just didnt understand the basic deffinition of derivitives i understand all the shortcuts just not the basic shit...
Feb 9 2009 12:34AM
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mr_shifty
Posts: 316 - Karma: 16
dead on

i just got raped on my calc test and i just finished the hw
Feb 9 2009 12:57AM
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ScuffDUFF
Posts: 2027 - Karma: 143
well i feel stoooopid
Feb 9 2009 1:19AM
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